Question

A ball falls freely from a height 1 meter to the ground and rebounced to a height of 0.8 meters . find the coefficient restution

Answer 1

The coefficient of restitution is 0.89

Explanation:

Given as :

The height from where a ball is fall = h = 1 meters

The ball re-bounced up to height = H = 0.8 meters

Let The coefficient of restitution = e

The value of g = 10 m/s²

According to question

∵ velocity of approach before collision= $V_a$ =  $\sqrt{2 g h}$

Or,                                    $V_a$   = $\sqrt{2\times 10\times 1}$

∴                                       $V_a$ = $\sqrt{20}$  m/s

Again

velocity of separation after collision = $V_s$ = $\sqrt{2 g H}$

Or,                                   $V_s$  = $\sqrt{2\times 10\times 0.8}$

Or,                                   $V_s$ = $\sqrt{16}$  m/s

∴                                      $V_s$   = 4  m/s

Again

coefficient of restitution = $\dfrac{velocity of separation after collision}{velocity of approach before collision}$

i.e                                   e = $\dfrac{V_s}{V_a}$

Or,                                  e = $\dfrac{4 }{\sqrt{20} }$

∴                                     e = 0.89

So, The coefficient of restitution = e = 0.89

Hence, The coefficient of restitution is 0.89  Answer

Answer 2

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