Question

A ball falls under gravity from a height of 10m with an initial downward velocity "u".It collides with the ground loses 50% of its kinetic energy in the collision and then rises back to the same height find the initial velocity "u"

• A. $14ms$
• B. $10ms$
• C. $11ms$
• D. $15ms$

Answer 1

Answer: (A)

$14ms$

Initial total energy at height h is, $=\frac{1}{2}m{u}^2+mgh$

Energy of ball after collision,

=50% of total energy.

As ball rebounds to same height h, then

mgh= 50% 0f total energy.

=$\frac{1}{4}m{u}^2+\frac{1}{2}mgh$

therefore, $u=sqrt\left(2gh\right)=14m/s$