Suppose at P point, a body loses its entire K.E which it had at O point and at Q point body losses 1/3 of its K.E which is at has at O. Find out the height h.

Use principle of conservation of energy

Total initial energy = Total final energy

Assuming O as reference of height measurement.

KE = 1/2mv^2 m is mass of the body and v is velocity of the body

PE = m x g x h m is mass of the body, g is acceleration due to gravity, h is height above

reference point of height measurement (O)

Initail energy at O = initial kinetic energy (KE) + initial potential energy( PE)( = zero since h is zero)

Final energy at Q = 1/3 initial KE + mgh ( h is height above point O)

KE + 0 = 1/3(KE) + mgh

mgh = 2/3KE = 2/3 (1/2mv^2) = 1/3mv^2

h = 1/3 (v^2/g) v is velocity at point O.