Question

A body is projected with the kinetic energy A rich that it's range is maximum.
Its potential energy at the maximum height is
1)E 2)E/2 3)2E 4)root2 E

Answer 1

given KE = E = 1/2 m u²

The Range is maximum for a given initial velocity u if the angle of projection Ф = 45°.

H = max height = u² Sin²Ф / 2g = u² * 1/2 * 1/2g = u² /4g

PE at max height = m g H = m  u² / 4  = E/2