chase
the maximun range of the projectile is reached when the launch angle is 45
degrees, so the height of the higher level which it lands on is not needed...if
it is lower or higher...the range is always going to be the maximum at 45
degrees.
banjov
NO MATTER WHAT THIER MAX RANGE WILL ALWAYS BE
REACHED AT AND ANGLE OF 45 DEGREES ANY ANGLE HIGHER
OR LOWER WOULD PRODUCE A SMALLER RANGE BUT A
GREATER VERTICLE DIStance
thanh911
wind direction and velocity matters too
jfagan
While the angle of 45 degrees produces the maximum range on flat ground,
we don't know the height of the landing. So we do not have enough
information to calculate the maximum range and the angle which will cause
it.
sheenago
The maximum range is achieved at a 45 degree angle so it could not land a
level higher than that.
noahg
45 degrees still maximizes the range
clampkin
The smaller the launch angle the farther the projectile goes, as seen in the
illustration in question one. It seems that no matter how high up the y axis
you drew a line, to simulate the higher level, that the previous statement
would still be true.
jcwhit
First of all, I took the horizontal as being a straight line from the landing
level to where it hits the projectile after it was launched. If the angle was
smaller than 45, the projectile would begin to level out then fall. I didn't
think that it could curve up either (making an angle > than 45. Therefore, if
it continued at 45 degree angle it would only get higher.
harif
The range is the horizontal distance travelled, and how high or low the
object will land does not change the horizontal distance traveled by the
object.
dlitvak
An angle larger than 45 increases the height that the projectile can reach, but
minimizes it's range.
bj17
If the object is going to end in a position higher than the firing point then the
whole equation is shifted to the new artificail horizontal, which is made by
conecting the firing point and end point with a straight line, and then
ajusting for gravity.
lopezk
We don't know how high its landing position is relative to its launch
position. Ideally, it would be 45 degrees on an even plane. Also, if the thing
launch can make it that high, 45 degrees would still give the max range. But
if 45 degrees can't make it to the higher level position, then the angle to max
its range is somewhere larger than 45.
zahar
The place of landing might be low enough to still be the legible landing
sight fot the projectile launched at the maximum range angle of 45 degrees.
However if the place of landing is high enouhg, the angle of the launch
should be adjusted to a higher angle.
elm2
If you fire a bullet at a very steep angle, it won't have a large enough
horizontal component of it's velocity vector to maximize its range.
Likewise, if you fire it at a very shallow angle, the vertical component will
be so small that it will hit the ground too soon to maximize its range. The
max lies at 45 degrees, the bisector of the angle made by the ground (your
landing spot) and the vertical (the direction that gravity acts upon the
bullet). So if you raise your landing spot, your angle will be smaller, and the
bisector of that angle will be a greater angle from the actual ground
timkucab
45 degrees will give the ideal vertical and horizontal components to launch
the projectile the farthest.
djpuzzo
Say that you are standing right next to a hill that has a greater slope than 45
degrees. If you throw it at 45 degrees you may hit the hill before the ball
reaches a maximum height, so if you throw it at a higher angle for such a
hill, it may go farther. However the hill may have a much smaller slope and
we may not have to use that as a factor.
elarrieu
i need to know Vo and the hieght of the landing area etc.
audreyr
Since the range is maximized at 45 under normal conditions, the destination
of the projectile vertically shouldn't matter, because range is concerned with
distance horizontally. Therefore, placing the target either above or below the
launching point won't affect how you maximize the horizontal distance, the
range.
mreskeni
Given that the ideal angle on level ground is 45 degrees one would expect
that if the projectile were shot onto higher ground then increasing the angle
would allow it to be in the air for a longer time over the raised ground there
by increasing the distance travelled by the projectile.
ikhanna
If the angle is smaller than 45 then the vertical component would be big.
mjctkd
I really don't have a reason. I just think it is still 45 degrees.
hessm
Realizing that 90 deg is the max angle for a forward directed projectile, 45
deg is half of 90, and would therefore be optimizing both the x and y
components of the projectile's motion.
kml13
It doesn't matter at what height level the projectile lands for the range to be
affected because these two components are independent of each other.
Therefore, the angle that maximizes the range remains the same, 45 degrees.
flynt
For the projectile to land on a surface higher then that of its launch position
it has to reach maximum height and come back down. Its max. height has to
be higher then the height of the surface. Reaching the height of the surface
depends on the angle of fire and the distance from the launch area to the
higher surface. If it is a sheer face for ex. with the cannon or what have you
directly at the base then an angle close to 90 degrees would be needed to get
it up there let alone abtain max. range along the horizontal.
rayyala
The greatest horizontal range can be found only at 45 degrees, no matter
how high the horizontal may be
nivzan
in order to achieve the same range the projectile must have more force and
an angle of 45 degrees in order to compensate on the distance of flight that
it can make where the higher level is found.
jswenson
45 degrees is the optimal angle. But you make the angle less than 45
degrees, the projectile may not go high enough to land on the higher level. If
the angle is greater than 45 degrees, the projectile may not travel far enough
horizontally to land on the higher ledge. If you knew how far away the ledge
was from where you were shooting the projectile and what it's height was,
you could figure out the best angle to shoot it at.
justynj
You would need to know how close the elevated surface is to the launching
point, what the elevation was of the landing point, and at what velocity it
was traveling.
smalcolm
The range is affected by the horizontal part of the objects velocity. This is
related to the sine of the angle and as you increase the angle, one increases
the sine and so one increases the range.
crivero
I believe that a smaller angle with the same force would allow the object to
travel further from the original position, giving it more area under its arc.
airflux
45 degrees is maximum that a flight can reach vertically, this is true because
with a lesser angle, the parabola reaches to a lower height, but eclipsing at
peak earlier, landing closer, this is the same for a angle above 45
sarika
Since there is a lack of specifics, I wonder how high the landing area is in
order to determine which angle will maximize the range. A larger angle than
45 degrees would decrease the range if on level ground, however I am
uncertain about the conditions since the landing area is of a different height.
monicad
If the level is much higher than the ground, the angle would have to be
larger. Otherwise it would be 45.
chown
With 45 degrees being the optimum angle for range, changing the angle
can't increase range. The vertical difference is irrelevent in this instance.
shazeeb
As the land level will be hogher on the landing site of the object, a greater
angle would cause the the object to travel a greater distance than at 45
degrees. Therefore, an angle greater than 45 degrees will give the maximum
range
ikhayal
You need to know how far away the landing site is and how high up because
this will affect the angle.
chalklet
If it was launched at a smaller angle, the apex would be lower. If it was
launched at a larger angle, the range would be smaller.
twong
the horizontal range is maximum fora launch angle of 45 degrees
mere1126
Making the angle larger than 45 degrees only makes teh object go higher, it
doesn't increase its horizontal distance. Making it smaller than 45 may cause
it to not reach the vertical height of its target.
npararas
An angle larger than 45 degrees would make the projectile stay in the air
longer which would give it more time to travel horizontally. If the angle
were smaller it would land sooner so that even though it's horizontal
component would be larger it wouldn't matter as much.
couguy
It depends how high the landing level is in comparison to the lauching level.
You may need to lauch at a larger angle than 45 degrees to make the ball
land on the higher level. Or mayber if the angle is less than 45 degrees you
can get the projectile to go farther.
kl3133
If the projectile lands at a level higher than its launch position, the angle
should be smaller than 45 degrees because the slope of tangent line is zero
at the highest point, and starts increasing as it falls down and the angle
became steeper
rume
I think it will still be 45 degrees as this is still the maximum range that
could be covered, unless the level is so high that it blocks the passage of the
projectile.
iansmith
If the projectile is fired from an angle great than 45 degrees, it will land
closer to where it was fired from, therefore, if it is fired at an angle less than
45 degrees, it will go more straight, and farther, than it would if it was also
fired up
dpitlor
We dont know how far away the platform is, and the initial speed also must
be known in order to answer the question.
leonadan
Because we saw that as ball is shot into the air it went hightest at that point.
pjung
If the height of the landing level is greater than the distance it is away from
the launch position, the anger must be greater than 45 degrees for the
projectile to even reach the landing level. In other cases, the angle can stay at
45 degrees to maximize flight time.
manishad
There is not enough information because if the projectile is to land on a
higher level then the height of this new level needs to be given.
agulsrud
Whether it lands higher than it started or not 45 degrees of an initial launch
will always result in the furthest horizontal distance
trosebud
The archs of the angles greater or less than 45 degrees always fall inside the
range of the 45 degree angled projectile at equivalent heights.
alconti
if the landing area is raised, shooting the projectile at a higher angle will
sacrafice distance at the cost of height. shooting the projectile at a lower
angle will cut hang time and distance even more if the landing area is raised.
given that the projectile has enough height when released at 45 degrees, it
will maximize its range.
czulu119
You would have to know other things like the initial velocity and more
importantly the change in height because 45 degrees might not be enough to
reach the higher level surface
ericmc
since the landing position is higher in order to reach the maximum distance
the angle needs to be increased
mohan
Range is the horizontal component of the fired projectile, so it is not
impacted by raising the level where the projectile ultimately lands. This
holds true with the assumption that the projectile can reach the higher level
with the 45 degree launch angle.
roosterh
Depending upon the height of the contact point, an angle greater than 45
degrees may produce a farther maximum range, but it is impossible to
know, unless we know how high the contact point is.
ctaclas
45 degree angle will still carry the projectile farther with the same ammount
of force...
cfalabel
If the landing area is on a higher level than the projectile's original launch
level (call this sea level). The projectile's flight time would be shortened by
landing on the higher level and it's range would be smaller than if it was
landing back at sea level. To insure that the projectile would at least land on
the higher level, the angle has to be increased to greater than 45 degrees. If
the angle was shallower, angle<45, the projectile would go under the higher
level landing area; but if the idea was to get the projectile to go far on sea
level, decreasing the angle would be the way to go.
rabu
Because when firing the weapon at 45 degrees from the horizontal, both the
vertical and horizontal components of velocity are maximized. The level of
the landing field is not necessarily important in this case.
kidcolin
Well, if the maximum range is achieved at 45 degrees on level ground, that
means that when you are shooting on to a higher surface that the projectile
has to cross the higher surface's horizontal at an angle of 45 degrees. This
means it's initial angle must be greater than 45 degrees.
erikd
The 45 degree angle would still go the furthest because it doesn't matter
where the ball stops vertically, it's still going to go further horizontally with
the 45.
livchako
because it said that a max range is achieved when launched at 45 degrees
dcrosy
The question just stated that when firing a projectile on level ground, which
is another way of stating the horizontal, the maximum range is achieved
when the launch angle is 45 degrees. Therefore the answer to the question
was already given as 45 degrees.
tnorton
you would need to know the initial vertical velocity of the launch, and also
how much higher the land site is than the launch site. an initial launch
degree of 45 might not be enough to even reach the land site.
sc
the vertical component and the horizontal component both contribute to the
scalar projectile motion. as the position of the object is intended to be
positioned above, more upward force is needed to produce a larger range
for the motion. a smaller angle than 45 would halp to rearrange the motion
to go upward more than going horizontally, compensating for the levation
of the final position.
aaronsev
I believe that it should actually be 45 degrees. If you look at the graphs of
the trajectories, you'll notice that at no point will an angle lower than 45
degrees cross the path of the 45 degree trajectory, so 45 degrees will have
always gone farther. Angles higher than 45 degrees will not go as far as long
as the projectile hits its maximum height.
cepalme
However higher the landing area is from the launching area, it is still going
to go further at 45 degrees than at any other angle, it doesn't really matter
that it lands in a higher point.
koff2
If the angle is smaller than 45 degrees then when it reaches the high point, it
has travelled a farther distance, therefore covering more ground, even on
higher ground.
johnmf
45 degrees will still maximize the range(assuming the projctile lands on the
ground(and does not hit an obstruction).
joejones
As understood in chapter 4 (projectiles in motion) 45* is the optimum
angle. However high the landing is take that hight and intersect it with the
projectile motion. This intersection creats an angle this should be 45 so the
original angle then must be greater than 45.
mmateja
If the projectile is to land on a level equal to its launch position, it is given
that the maximum range is achieved when the launch angle is 45 degrees.
Even if the projectile were to land at a level higher than its launch position,
the maximum range would still be highest when launched from 45 degrees,
it doesn't matter where the projectile lands. The x variable will only get
smaller when thrown from a higher or lower angle.
bant
The problem cannot be solved without knowing how higher is the level that
the projectile will land on. This is because if the projectile is to launch at an
angle < 45 than it will achieve its highest range, but depending on how high
the level is the projectile might hit the front of the level and not achieve its
highest range.
mogilka
In order to find the maximun distance you need to know how high the level
is that the projectile is landing on.
eaviles
To hit a point at a higher level, you need to both increase the velocity and
the angle. Because if you only increase the angle then it will come up short,
because more of the velocity is in the vertical component now. so by adding
more velocity we will still go the same distance, but now at a higher level.
bcassell
there is not enough information, becuase you must know the elevation of
the landing point, and at what distance the elevation begins, because
depending on how hi it is, a higher angle may be able to overcome the cliff
while a small angle cannot. while on the otherhand, if its not that hi, an
angle less than 45 will still go farther than an angle greater than 45.
amymar
The smaller the angle, the farther the projectile will travel.
dianis
a higher level could mean 5cm higher or it could mean a trying to shoot the
projectile to the top of a large cliff. In the cliff case, a 45 degree angle may
not allow the projectile to clear the cliff, it will hit the side, while an angle
larger than 45 will allow it to clear the cliff. If the projectile lands a very
small distance (say 5cm) above its launch point, the angle will be almost
exactly 45.
bdsachs
In most situations, I believe it would still be the 45 degree angle. The reason
for my response is the off chance that the 45 degree angle would cause the
projectile to encounter some obstacle (the side of a mountain) that could be
avoided by a greater angle. If it were not for the clearance issue, I believe
that 45 degrees would always yield the farthest flight. I cannot think of a
situation in which a smaller angle would be accurate, unless one would
have to avoid a collision with something above, like hitting a golfball out
from under a bridge where a 45 degree or greater flight would cause a
collision with the underside of the bridge.
rzipagan
It will always achieve the largest range when it is 45 degrees at the
horizontal.
gbrun
At 45 degrees, the maximum range is achieved on a flat surface. However,
if at 45 degrees the projectile is not blocked by the higher level, than 45
degrees should be the best angle. But it would depend on how close the
higher level is to the launching level and how high it is!
mitesht
The information that is not given is at what height the landing platform is. If
it is too high, then the flatter angles would run into the side of the "cliff"
and never make it to the platform itself.
tamadio
If you throw the projectile at a lower angle it has a better chance of going
further. It's like your trying to throw this projectile through a hoop and if
you undershoot the hoop youll get the ground but if you aim too high you
will waste much of your velocity just hanging in the air.
ebaker
The location of the projectile is irrelevant. The maximum angle is still 45
degrees.
xtzhang
Because the projectile lands at a level higher, the launch angle should also
be bigger. I am not quite sure though.
mrodrig8
Assuming that the new surface does not block the trajectory a 45 degree
angle would be best because it would retain the best trajectory and
hopefully just barely clear the mountain. If the new surface was higher and
blocked such a trajectory then more information would be needed.
tchyn82
regardless of whether it lands on a higher surface than the level ground the
fact of the matter is that we know that it lands meaning that the elevated
surface won't obstruct the prjectiles motion meaning we don't have to
change the angle to avoid this elevated ground. 45 degrees will maximize its
range.
bdolan
Rather than considering that the projectile lands on higher ground, consider
that there is a "dip" where the projectile is fired from. When the projectile is
out of the dip and level with the landing point, the best angle would be 45
degrees. To achieve this angle at this point, The original firing angle must
have been one larger than 45 degrees.
imcnulty
If the projectile was shot from a 45 degree angle, it would hit the ground
sooner at the higher level than if it landed on the same level from which it
was fired. You need to increase the launch angle in order to compensate for
this change in the level of the ground.
cheymann
it depends on how high the level is
kamran
I don't think that it is possible to answer this question without knowing the
initial velocity components of the verticle and horizontal
bwelch
Just because the landing place was at a higher elevation, doesn't mean that
the distance travelled is changed at all... it still goes the maximum distance
per angle.
avshah
There is not enough information because you need to know the components.
You need the vertical and horizontal component in order to see what the
projectile looks like.
comper
There is not enough information because it is possible that the surface is
higher than can be reached by the maximum height of the projectile when
launched from 45 degrees.
cmoore
A higher angle would still give you a smaller range (higher angle would be
better if you were merely trying to reach a higher level) and a lower angle
may not even make it to the higher level.
jaberlin
If the launch level is higher, then the y component of the projectile must be
increased. Since in this problem the maximum launch angle at ground level
to ground level is 45 degrees., the new angle must be larger because the x
component would have to remain the same, so the y component must
increase. I wish I could draw a picture. It would be much easier to explain
visually.
dainowsk
no matter where the object lands and angle of 45 degrees will maxime the
distance
abell
In the formula for horizonal range, height of the landing surface is not taken
into account. Therefore, 45 degrees would still be the angle that would
maximizes range.
shouston
The question depends on the height of the ground above the launch position.
If the ground is only slightly higher than the launch position, then the 45
degree angle will still maximize the range. However, if the landing ground
is considerably higher than the launch position, then an angle greater than 45
degrees will maximize the range.
lsstoke
In order to maximize the range one must increase the vertical component of
the projectile vector. Therefore, increasing the vertical component increases
the angle.
rseth
The question is unclear on what the horizontal is. I don't understand what
exactly its asking for.
ndeveau
if you don't know how high the projectile has to reach (the height of where
it will land) you don't know the degree of the angle it would take to clear
the higher position and increase the range
wildwood
Well, it definitely depends on the height and how far from the position this
higher level is. My initial guess was 45 degree angle, but, upon second
thought, if the height was close to the launch position, a bigger angle would
be better.
arkman
I believe that a lower than 45 degree trajectory will go further than a higher
than 45 degrees, because it will have a greater Vx even though it will stay in
the air less time. The reason that the answer depends on more information is
that if the angle is so low that the projectile doesn't make it up to where the
target is, say you fire at a wall that is 100 feet high and 1 foot in front of
you, in order to make it up that high, you need an angle much greater than
45 degrees.
rr2itali
45 would still be the ideal angle since the projectile shot at another angle
would land before the projectile shot at a 45 degree angle on level ground,
the same would be true for higher ground and perhaps the projectile at
another angle may not even reach the higher ground
jessicag
It does not matter what level the projectile lands on, (excluding if it
completely misses the level), because the maximum range will always be
achieved when the launch angle is 45 degrees. The range will be greatest at
this angle for the projectile's entire course
cait54
The projectile moves farther horizontally according to the size of the launch
angle. The smaller the angle, the farther, horizontally, it takes to reach the
projectiles maximum height. The projectile's distance is increased with the
decrease in the launch angle.
svanas
If 45 degrees gives the maximum range than this would be the case for
shooting a projectile up to a higher level of elevation. If the angle was less
than 45 degrees the projectile could hit the incline due to the lack of
velocity in the vertical direction. If the angle was greater that 45 degrees it
may clear the incline but the total range would be less. If the projectile
didn't clear the incline then the angle would not matter as all projectiles, if
launched at a high enough velocity, would have to stop at that point as they
could not continue their motions through the hill.
jjevans
All objects are effected by gravity equally, so the height has no effect on the
range
lhhoward
The angle needs to be greater than 45 degrees, so that the the greater
Y-component can compensate for the higher ground it is going to land on.
The projectile will not go as far as it did on level ground, but, for the height
of the landing ground, it will be maximized. If the angle was less than 45
degrees then the projectile would hit the ground too early, possibly even
before it reaches the higher ground. This of course depends on the angle.
The closer to 45 degrees it gets, the farther it will go.
tashkent
Changing the angle will not make the projectile go farther but will only
shorten the range. The change in the velocity is needed for this problem, but
it is not given.
smccurdy
A 45 degree angle gives the maximum range for a projectile. as the equation
for range shows, an angle of 30 degrees and 60 degrees has the same range,
and likewise launch angles of 75 degrees and 15 degrees also have equal
ranges (and thus equal horizontal components of motion), although the
larger angle achieves a greater maximum height (it has a greater vertical
component of motion). Assumimg a projectile launched at 45 degrees has a
large enough vertical component of motion so it can clear the raised
platform, it will still have the maximum range because all other launches
will still at that ending height be travelling on parabolic paths with slower,
lesser horizontal components of motion. However, if the landing platform
is raised very very close to the launch platform, and raised very very high, a
45 degree angle will not allow the projectile to clear the raised plaform
because it's vertical component of motion will be insufficient. In that case a
launch angle greater than 45 degrees must be used to achieve the maximum
range, because smaller angles will, in essence, bump into the side of the
platform instead of landing on it. Without the initial velocity of the
projectile, the height of the landing platform, and the position of the landing
platform, one cannot determine if a projectile launched at the angle of 45
degrees can clear the landing platform so it can achieve the maximum
possible range.
mduff
You don't know how high the surface is or the initial velocity.
balfon
It all depends on the actual height of the target. Depending on where the
projectile is fired, the angle needed to hit the target can vary greatly. If there
is a great obstacle between you and the target, you may need an angle much
higher than 45 degrees to clear the obstacle. It's also possible that the target
is very close or even at a lower altitude that it would need less than 45
degrees to hit the target.
catiq
If you shoot it at a higher angle the range will be too small to reach the
higher level, and if you shoot it at a smaller angle the object may not be high
enough to reach the higher level.
lilylam
the maximum value for the range occurs when sin 2data = 1 or 2data = 90
degrees... the launch angle (data) therefore equals to 45 degrees.
hgg
the greater the angle the shorter it travels
tgelito
There is not enough information because we do not know the height of the
landing position so we could not find its maximum range.
stephpry
The answer depends on the height that you are trying to reach with the
projectile.
datars
The ground is higher, so the vertical component must be increased, which
would result in an increased angle.
johnok
the max range is achieved by firing at an angle of 45 degrees. It doesn't
matter if it lands on a higher level, because no mater what angle you fire at
it will land on the same level just at different ranges. the ranges will all be
shorter then if fired on a level field but the 45 degree angle with produce the
longest range. The only problem is if the angle is too low and the projectile
doesn't clear the level. But this is not a factor in this problem.
jontam
because it lands at a higher level, so the angle of the launch position should
be a little bit smaller in order to get max range
tokamoto
Because you don't know how high the landing grounding is.
ajaytom
It is not possible to answer this question because you need the vertical and
horizontal component of the initial velocity.
aparish
Even if the landing ground is higher than the firing ground, a 45 degree
angle would acheive maximum range, as the arc formed acheives greater
displacement, even if evaluated at a y value other than 0.
nbarbosa
It's because once the projectile is launch and lands on the level higher. Just
draw a dash line from the level to the initial launch of the projectile, from
the line add 45 degrees and draw a line from the dash to initial level of the
launch and it will be greater than 45 degree and gives a larger range.
tlbolles
Because you don't know the height of the higher level, you can't say that
forty-five degrees would maximize the range.
gstria
In my opinion, the final height that the projectile is fired to does not affect
the angle which maximizes distance. The only time the final height would
matter is if the final height is lower than the intial height. However, because
this is not the case, it will not change the angle.
aeugley
If the level that the projectile is landing on is much higher than the initial
height, is close to the projectile, and at a sharp incline, then the projectile
may not ever reach a height of that unless you raise the angle of the
projectile. However, if the height is not huge then the maximum length is
acheived at 45 degrees.
lisa727
since the projectile is being fired at a angle of 45 degrees the only way the
projectile can land farther is if the angle is smaller because the ratio of the
change in y over the change in x increases as the angle gets smaller.
tan(angle)= y/x becasue as the angle gets smaller the tangent gets smaller
and as a result the x (horizontal range) increases.
pvodov
To achieve the maximum length on either a flat, or a raised surface, you still
need to go for the maximize the horizontal component of velocity, and that
is done in every case by shooting the projectile at a 45degree angle
ty420
The reason there is not enough information is because the higher level may
be above the path of the projectile of 45 degrees. Therefore, that angle
would not be able to be used because the projectile will never reach the
higher ground. However, if the higher ground was below the projectile path
for 45 degrees, then that angle would be the correct one to use. Therefore,
there is not enough information to answer the question correctly.
socrates
A larger angle is needed to ovecome the slope the projectile is climbing
meilah
I don't really understand the question, what does "landing at a level higher
than its launch position mean." I interpret it to mean that it lands just a bit
farther from its launch position so I think that if the object just wants to be
slightly farther away, then it would have to be thrwon at a larger angle than
45 because if you through it at a 90 angle, it would be at its same position
emhoff
despite the difference in height from the launch position, it is still defined
that the projectile will have a maximum range from a 45 degree angle.
canndel
if the angle is greater than 45 degrees the range will still be small because of
the large vertical component, and if it is less, then it may not make it over
the raised surface, so the maximum range should still be 45 degrees.
jnaacnkc
I'm not sure if my answer was right. I decided the answer by using the
common sense
selija
If the projectile is to be fired onto a higher level than its launch position,
then it needs a higher trajectory angle to maximize its range when it hits the
higher level ground.
amarsh
If you launch the projectilre at a smaller angle the increased horizontal
component will make up for the decreased verticle components.
ecarrel
If the projectile lands at a height higher than that which it took off at, the
projectile will not be airborne as long as if it landed at the height from
which it took off. What needs to be done is to guarantee that the horizontal
component of the velocity has the maximum effect on the projectile before
it lands. In the case of question 2, because it lands at a higher level, the
projectile needs to be launched at a angle somewhat greater than 45 degrees,
so that air time is maximized, and the projectile has the ability to travel the
farthest distance forward.
apisco
There is no guarantee that an angle larger than 45 degrees can even reach
that same point. Also, there is no guarantee that the angle smaller than 45
degrees will go high enough to reach the point.
cflam
It does not matter if the projectile lands on an elevated surface, the largest
range still results from 45 degrees.
stark
Say you have 3 objects shot with the same intial velocity from the same
point at and angle more than 45, less than 45 and 45. By the time they reach
their respective maximum heights, the 45 degree object will be farther from
the intial point than the other two, so anywhere it lands on it's negative
trajectory will be at a greater distance than the other two.
hetfield
The new angle would be 45+x where x is the angle formed between the
horizontal and the line between the origin and the landing spot.
elio
The reason I chose answer 4 is that the launch angle is dependent on the
height of the target. For example, if the target is situated at 3 feet away and
300 feet high, the necessary angle will be far greater than 45 but if the angle
is too low it might not clear the elevated target.
wshaw
The maximum distance the projectile will travel with a given angle on
non-level ground will depend on the elevation of the ground where the
projectile is being fired. If the difference in elevation is small, then an angle
closer to, but a bit higher than 45 degrees. If the difference in elevation is
great, then a much higher angle is needed to prevent the projectile from
hitting the terrain stunting its ability to travel.
araquel
i dont think that the y matters when the maximum displacement it is
measuring is the range (x values)
jmonte
you would increase the angle in order to accomidate for the increase in
altitude of the landing area.
tmzap
The maximum range is only one path that the projectile can take, so it
doesnt matter where on the path the projectile stops, that point will still be
the farthest it can go.
andi1
If a projectile lands at a level higher than its launch postion, the angle must
be 45 degrees to maximze the range. If the angle was smaller than 45
degrees it would not reach the higher level, but if the angle was greater than
45 degrees it would reach the higher level, but the range would be shorter.
kswiercz
The forty five degree angle stiil allows the particle to travel the farthest
because no matter the height the pariticle is achieving the ideal trajectory.
jaredg
There isn't enough information given because in order to maximize the
range you need a higher velocity as well as a higher angle of trajectory.
sona09
45 degrees is the angle at which maximum range will be attained at normal
ground. Knowing that, I assume that it will be the same for an object
landing on slightly higher ground. However, there is some uncertainty
because we don't know how much higher the ground is. That could be an
influencing factor if the height is extremely great.
dvhn
The maximum range is always determined when the angle is 45 degrees.
Any angle more or less that 45 degrees makes the bullet shy of maximum
distance "X."
brufleth
It could be hitting a wall or steep step like structure and if had a great
vertical component it might be able to make it over or onto a higher part of
the terrain.
ejc
The range of the projectile is the displacement along the x-axis and is
maximized at an angle of 45 degrees. Changing the height of landing
(displacement along y-axis) does lessen the displacement along the x-axis,
but this change is because the time of the projectile in the air is lessened, not
because of any change in angle. Therefore, the displacement of the projectile
on the x-axis is still maximized at an angle of 45 degrees.
rhurt
HIgher angle, it would land closer to it's origin, and a smaller angle, it
wouldn't clear the cliff.
leotess
45, object will still fly the furthest at that angle bc if you look at its path the
only thing that will change is that its landing is not going to be at 0, but
depending on hte height of landing mark, the object will still get there the
fastest at 46 degrees
trego
Its range will be greatest when fired at a 45 degree angle regardless of the
level that it lands on assuming that a 45 degree angle sends it high enough
to reach the higher level in the first place.
naomiq
If the object has to land at a level which is higher than where it is being
launched, then the object has to be aimed higher than it is now.
svasquez
I believe that an angle smaller than 45 degrees would maximize the range if
having to land on a higher level because this smaller angle will make the
launched object fly through the air a longer time and will finally land when
it is just about to fall from its highest point.
griffinb
If it is shot less than 45 it won't make it high enough to land on the
platform, and 45 won't be as effective as a higher angle because the object
has to be high enough to landon the platform.
rmalhash
for the projectile to land at a level higher than it was origionally it needs to
have an angle more than 45 degrees and also if the angle was lower than 45
degrees then it wouldn't launch at a position at a higher level.
joines
No matter how you change the angle, the velocity will be the same. So if
you make it less than 45 degrees, the object will not stay in the air as long. If
you increase the angle, you lose distance but gain height and time of flight.
dmarkz
Since the ground increases in angle the projectile must be fired in the same
increasing angle as the ground to get the maxium distance.
akyar
i can't put that in words, I have to draw it
cfarris
45 degrees will always be the angle that maximizes the range fired since it
maximizes ratio of time in the air to distance traveled, thus giving
maximum range.
jenhen
If the angle is increased, the projectile will just go higher rather than farther.
If it is decreased, the projectile might not reach the height needed.
sassan20
I choose 4 because both choice 1&2 could be true for this question. My
reason for this is that since 45deg reaches the highest R, it can always reach
the new Maximum R as long as the elevation of ground doesn't exceed the
Y max of projectile 45deg. At the same time since projectile lands on higher
ground it means that the new Range is shorter, so an angle that is greater
then 45deg would also reach new Max R. Since we don't know how high the
land is we can't rule out 45deg. But surly choice 2 is correct at this case, but
we can't rule out choice 1 for lack of information.
hchow
from the question, it already states that the maximum range can be reached
when the launch angle is 45 degrees. even though the projectile will be
landing on a higher level, it does not affect the launching angle.
douglasd
When adjusting the angle of the launch position you are exchanging vertical
component for horizontal component. Although you can achieve the height
needed by increasing the angle, this detracts from the vertical distance
reached. Therefore, one can not be certain, with the limited information, if
the distance covered by increasing the angle is still enough.
rosalyn7
to maximize the range, it should not matter what level the ground is in
which it lands. 45 degrees will maximize the range
jiayi
I chose answer 1 (45 degree) because no matter where the projuctile lands,
45 degree angle will always give the maximun value of Vx and Vy to
maximizes the range even thoung in this case, the range will become
smaller. The maximun value for sin 2O is 1, so the angle should be 45
degree.
milig
triangle rules
shareef
Greater initial speed is required for the projectile to move further plus
greater angle than 45 degrees. The question doesn't mention any change in
the initial velocity.
kingjohn211
Because the height at which the projectile lands is unknown it is unable to
say what angle would maximize the distance.