Question

A body of mass 4kg moves with a velocity of 15m/s collide elastically with a body of mass 8kg is at rest,then the velocity of 8kg is

Answer 1

The velocity of 8kg is 10$(\frac{m}{s})$.

Explanation:

1. Let

  initial velocity of 4 kg mass $u_{1}$ =15$(\frac{m}{s})$.

  initial velocity of 8 kg mass is $u_{2}$ = 0$(\frac{m}{s})$.  

  final velocity of 4 kg mass is $v_{1}$.

  final velocity of 8 kg mass is $v_{2}$.

2.  During collision total momentum is conserved.

    Means

    Initial Momentum = Final Momentum

    $m_{1}u_{1}+m_{2}u_{2}=m_{1}v_{1}+m_{2}v_{2}$

    So

   4×15+8×0= $4v_{1}+8v_{2}$        

   After solving we got

  15 = $v_{1}+2v_{2}$          ...1)

3. From

Coefficient of restitution = $\frac{Relative velocity of separation}{relative velocity of approach}$      ...2)

Here collision is elastic, so coefficient of restitution is 1.

4. So from equation 2)

   $1= \frac{v_{2}-v_{1}}{u_{1}-u_{2}}$

  $1= \frac{v_{2}-v_{1}}{15-0}$

So

$v_{2}-v_{1}$= 15        ...3)

5. After solving equation1) and equation 3)

  We got

  $v_{2}$ = 10$(\frac{m}{s})$= velocity of 8 kg mass.