Question

In the absence of air resistance, a projectile is launched from and returns to ground level. It follows a trajectory similar to that in the figure below and has a range of 15 m. Suppose the launch speed is doubled, and the projectile is fired at the same angle above the ground. What is the new range?

Answer 1

range will be proportional to speed,and time in air.

so how does speed affect time in air?

consider time in air...
hf=h0 + vosinTheta*time-1/2 g t^2

0=0+ t(V-1/2 g t)
so t=2V/g so time in air is directly proportinal to initial speed.

range is then proportional to v^2
so if it was 15m, it is now 15*4 since speed was doubled

Answer 2

In the absence of air resistance, a projectile is launched from and returns to ground level. It follows a trajectory similar to that shown in the figure below and has a range of 17 m. Suppose the launch speed is doubled, and the projectile is fired at the same angle above the ground. What is the new range?