A ball is dropped from some height. It bounces off the floor and rebounds with a speed that is one-half the speed it had just before it struck the floor. How high will the ball rise compared to the height from which it was dropped

The correct option is C

Explanation:

According to third equation of motion, v

2

=u

2

+2ax

Here, u=0 m/s

a=−g and x=−h

Negative sign indicates downward direction. Displacement and acceleration both are downwards.

So,v=±

2(−g)(−h)

We take minus sign because it is downwards.

v=−

2gh

After bouncing. velocity becomes 80% of v, i.e.,

v

′

=+0.8

2gh

(positive sign because the direction of ball has reversed after bouncing and is upwards.

Applying third equation of motion again, for u=v

′

, v=0 and a=−g

v

2

=u

2

+2×a×x

Thus,

0=0.64(2gh)+2(−g)x

or

x=0.64h

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