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 vo sinθ g

Therefore the range is:

2 vo2 sinθ cosθ g

Using the identity 2 sinθ cosθ = sin 2θ gives:   Range

=

vo2 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?

1. The green ball goes twice as far
2. The green ball goes 4 times further
3. It depends on the ratio of their masses