A projectile is fired with fixed speed u from the top of a cliff of height h. The angle of projection may be chosen freely.
If u² = gh, the maximum possible horizontal distance from the foot of the cliff before the projectile hits the ground is:

Question

A projectile is fired with fixed speed u from the top of a cliff of height h. The angle of projection may be chosen freely.

If u² = gh, the maximum possible horizontal distance from the foot of the cliff before the projectile hits the ground is:

G1 Physics · Accepted Answer

For projection from height h, the maximum horizontal range for a fixed speed u is R m a x R_max R m ​ a x = (u/g)√(u²+2gh). Given u² = gh, R m a x R_max R m ​ a x = (u/g)√(3u²) = √3·u²/g. Since u²/g = h, R m a x R_max R m ​ a x = √3 h.