This is a two dimensional problem. In a science fiction story, the acceleration

Question

This is a two dimensional problem. In a science fiction story, the acceleration due to gravity on an alien planet does not point straight down. Instead it points down and to the right at a 45 degree angle below the horizontal. A projectile is launched horizontally to the right with an initial speed v from the top of a cliff of height h. Determine the simplest expression for the horizontal range of the projectile in terms of g, h, and v. The simplest expression will have one small fraction and be factored completely. Note: use the basic kinematic equation for constant acceleration.

Explanation / Answer

for the protectile

here let V be the speed and angle theta= 45 deg

so also let the maximum height is H

Using third equation of motion

v^2 - u^2 = 2 * g * (H - h)

0 - ( V * sin(theta))^2 = -2 * g * (H - h)

H = h + (V * sin(45))^2/(2 *g)

maximum height attained by the projectile is

H = h + V/4g

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