Question

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 Figure 3.10 and has a range of 29 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

In the vertical:
vf=vi-gt where t is time in air.
because vf=-vi in the vertical
t=2vi/g

Now, horizontal distance
d=vih*t=vih*2vi/g

now if vi is doubled, vi (in the vertical and horizontal) are doubled, so
d= is 2^2 as far, or four times as far. it is in the air twice as long, and its horizontal velocity is doubled.