Question

A ball falls under gravity from a height of 10 m with an initial downward velocity u. It collides with the ground, losses 50% of its energy in collision and then rises back to the same height. The initial velocity u is:

• A. $7ms^{- 1}$
• B. $25ms^{- 1}$
• C. $14ms^{- 1}$
• D. $28ms^{- 1}$

Answer 1

Answer: (C)

$14ms^{- 1}$

Answer 2

If m is the mass of the ball, then its total initial energy at height h.

$= \frac{1}{2}mu^{2} + mgh$

Energy after collision = 50% of $\left( \frac{1}{2}mu^{2} + mgh \right) = \frac{1}{2}\left( \frac{1}{2}mu^{2} + mgh \right)$

As the ball rebounds to height h, so.

$= \frac{1}{2}\left( \frac{1}{2}mu^{2} + mgh \right) = mgh$

Or $\frac{1}{4}mu^{2} = \frac{1}{2}mgh$

$u = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 10} = 14ms^{- 1}$