Range
The range, the horizontal distance until impact, is: x = v_{x}(0) t = v_{o} cosθ
t,
where the time of flight t is given by: t 
= 
2 v_{o} sinθ
 
g


Therefore the range is: 
2 v_{o}^{2} sinθ cosθ
 
g


Using the identity 2 sinθ cosθ = sin 2θ gives: Range 
= 
v_{o}^{2} sin 2θ
 
g


Two balls are launched with the same initial angle. The green ball has an
initial velocity twice as large as that of the red ball. How do their ranges
compare?
 The green ball goes twice as far
 The green ball goes 4 times further
 It depends on the ratio of their masses