Question

if the energy of a ball falling from a height of 10 metres is reduced by 40% how high will it be found

Answer 1

Let E be the energy of the ball falling through a height of 10m

E = mgh (potential energy) 
E = m(9.8)(10)
E = 98m J ; (where m = mass of body.)

now let’s suppose the body losses 40% of its energy and rebounds back to a height of “h1’ and its new energy is “E1” which is 60% of the initial energy “E”

E1 = 60% (E)

also

E1 = mgh1 (the mass remains the same)

=> m(9.8)h1 = 60/100 ( 98m)

the m’s cancel out.

Therefore, 
9.8 (h1) = 0.6 (98)
h1 = 0.6 (10)
h1 = 6m.