A ball is projected vertically down with an initial velocity from a height of 20 m onto a horizontal floor. During the impact it loses 50 % of its energy and rebounds to the same height. The initial velocity of its projection is

Question

A ball is projected vertically down with an initial velocity from a height of 20 m onto a horizontal floor. During the impact it loses 50 % of its energy and rebounds to the same height. The initial velocity of its projection is (A) 20 ms-1 (B) 15 ms-1 (C) 10 ms-1 (D) 5 ms-1

Tardigrade Admin · Accepted Answer

Let ball is projected vertically downward with velocity

v

from height

h

Total energy at point

A = \frac{1}{2} m v^{2} + m g h

During collision loss of energy is

50%

and the ball rises up to same height.
It means it possess only potential energy at same level.

50% (\frac{1}{2} m v^{2} + m g h) = m g h

\frac{1}{2} (\frac{1}{2} m v^{2} + m g h) = m g h

v = 2 g h = 2 \times 10 \times 20

∴ v = 20 m / s

Q. A ball is projected vertically down with an initial velocity from a height of $20 m$ onto a horizontal floor. During the impact it loses $50%$ of its energy and rebounds to the same height. The initial velocity of its projection is

$20 m s^{- 1}$

$15 m s^{- 1}$

$10 m s^{- 1}$

$5 m s^{- 1}$

Q. A ball is projected vertically down with an initial velocity from a height of 20m onto a horizontal floor. During the impact it loses 50% of its energy and rebounds to the same height. The initial velocity of its projection is

20ms−1

15ms−1

10ms−1

5ms−1

Q. A ball is projected vertically down with an initial velocity from a height of $20 m$ onto a horizontal floor. During the impact it loses $50%$ of its energy and rebounds to the same height. The initial velocity of its projection is

$20 m s^{- 1}$

$15 m s^{- 1}$

$10 m s^{- 1}$

$5 m s^{- 1}$