A ball is thrown vertically downwards from a height of 20 m with an initial velocity 
. It collides with the ground, loses 50 percent of its energy in collision and rebounds to the same height. The initial velocity 
is 
Take 
Text Solution
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: The situation is shown in the figure. Let v be the velocity ofthe ball with which it collides with ground. Then according to the law of conservation of energy,
Gain in kinetic energy 
loss in potential energy i.e. 
(where m is the mass of the ball)
or 
(i) Now, when the ball collides with the ground, 50% of its energy is lost and it rebounds to the same height 
or 
Substituting this value of 
in 
(i), we get
or 
or 
Here, 
and 
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