Question

Consider a projectile fired horizontally from a cliff of a given height. With what speed must it be fired so that it makes a 45 degree angle with the ground when it hits

Answer 1

It hits ground with 45° angle when the vertical velocity, vy, is the same as the horizontal velocity, vx, which equals u (initial velocity) if the projectile is fired horizontally and ignoring air-resistance.

vx=u

Let H=given height of cliff
vy²-0²=2gH
vy²=2gH
since vy=u,
u²=2gH
u=√(2gH)