Question

A ball is thrown with a velocity of 6 m/s vertically
from a height H = 3.2 m above a horizontal floor. If it
rebounds back to same height then coefficient of
restitution e is [ g = 10 m/s?]
(1) 0.5
(2) 0.6
(3) 0.7
(490.8​

Answer 1

Answer:

(Option D) 0.8

Solution:-

Velocity=6 m

Height=3.2 m

G=10 ms^-2

So

Velocity of ball just before hitting the ground

${v}^{2} = {u}^{2} + 2gh$

${v}^{2} = {6}^{2} + 2 \times 10 \times 3.6$

${v}^{2} = 36 + 64$

${v}^{2} = 100$

$v = \sqrt{100}$

$v = 10 \: m {s}^{ - 1}$

A rebound back to same height then coefficient of restitution on ground

$= \sqrt{2gh}$

$= \sqrt{2 \times 10 \times 3.2}$

$= \sqrt{64}$

$8 \: m \: {s}^{ - 1}$

Coefficient of restitution

$= \sqrt{ \frac{ k_{e} \: after \: impact}{ k_{e} \: befor \: impact } }$

$= \sqrt{ \frac{ \frac{1}{2}m {v}^{2} }{ \frac{1}{2}m {v}^{2} } }$

$= \sqrt{ \frac{ {v}^{2} }{ {u}^{2} } }$

$\frac{8}{10} = 0.8$