Projectile motion is motion under the influence of gravity alone.

A thrown object is a typical example. Follow the motion from the time just after the object is released until just before it hits the ground.

Air resistance is neglected. The only acceleration is the acceleration due to gravity.

Let's say you're on top of a cliff, which drops vertically 150 m to the ocean below. You throw a ball with an initial speed of 8.40 m/s at an angle of 20 degrees above the horizontal.

(a) How long does it take before it hits the water?

(b) How far is it from the base of the cliff to the point of impact?

As usual, be as systematic as possible. Draw a diagram, choose a coordinate system, and organize your data.

Origin: the base of the cliff

Positive directions: +x right and +y up

(a) How long does it take before it hits the water?

Use the y-information to find the time of flight. One method is to do it in two steps, first calculating the final y-velocity using the equation:

v_y ² = v_oy² + 2 a_y (y - y_o)

This gives v_y ² = 2.873² + 2 (-9.8) (-150) = 2948.3 m² / s² . Taking the square root gives: v_y = +/- 54.30 m/s.

Remember that the square root can be positive or negative. In this case it's negative, because the y-component of the velocity will be directed down when the ball hits the ground.

Now find the time using:

v_y = v_oy + a_y t

So, -54.30 = 2.873 - 9.8 t, which gives t = 5.834 seconds. Rounding off, the ball was in the air for 5.83 s.

(b) How far is it from the base of the cliff to the point of impact?

Plug the time we just calculated into the equation:

x - x_o = v_ox t + ½ a_x t²

x = (7.893) (5.834) = 46.0 m.

A hunter spies a monkey in a tree, takes aim, and fires. At the moment the bullet leaves the gun the monkey lets go of the tree branch and drops straight down. How should the hunter aim to hit the monkey?

1. Aim directly at the monkey
2. Aim high (over the monkey's head)
3. Aim low (below the monkey)

Note that a complete analysis of the problem can be found in the textbook.