Question

if the energy of a ball falling from a height of 10m is reduced by 40% how high will it rebound

Answer 1

the ball is dropped from a height, h1 = 10 m
Potential energy at h1 = mgh1
Given g =10 m/s2 , h1 = 10 m
Therefore the potential energy at h1 = m×10×10
= 100m J
On striking the ground level, the ball looses 40% of its initial energy:
i.e. (40/100)× 100m J
=40m J
he energy left on striking the ground = 100 m J - 40 m J
= 60 m J
So the final energy of the ball , mgh2 = 60m J
i.e h2 = (60 /10) = 6 m
Hence the ball will bounce back to a height of 6 m

Answer 2

h=10m
g=10m/s^2
Potential energy=mgh=m*10*10
=100*m
Energy reduced = 40%
Energy left=60%
>60% of 100*m
=60/100*100m
=60*m
60m=mgh
60/g=h
h=6metres


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