A stone projected vertically upward with a velocity 'u' reaches a maximum height 'h'. Find the ratio of kinetic energy and potential energy of the stone, when it is at height 3h/4 from the ground..?

Initial velocity = u

Acceleration = g

Now, at maximum height ‘h’,

0² = u² - 2gh

=> h = u²/(2g)

If the velocity at height 3h/4 is ‘v’ then,

v² = u² – 2g(3h/4)

=> v² = u² – (3/2)gh

=> v² = u² – (3/2)(g)(u²)/(2g)

=> v² = u² – (3/4)u²

=> v² = ¼ u²

So, KE at that height is = ½ mv² = ½ (m)(¼ u²) = (1/8) mu²

PE at that height is = mg(3h/4) = (m)(g)(3/4)(u²)/(2g) = (3/8) mu²

So, ratio of kinetic to potential energy at that height is = (1/8) mu² : (3/8) mu² = 1 : 3