Question

A prticle of mass $m$ moves with velocity $v_0=20\text{m/s}$ towards a large wall that is moving with velocity $v=5\text{m/s}$ towards the particle as shown. If the particle collides with the wall elastically, then find the speed of the particle just after collision. (Assume collision with the wall is elastic)

• A. $30\text{m/s}$
• B. $20\text{m/s}$
• C. $25\text{m/s}$
• D. $22\text{m/s}$

Answer 1

The correct option is A $30\text{m/s}$

As we know
$e=\frac{v_{2f}-v_{1f}}{v_{1i}-v_{2i}}$
(Take positive motion towards right)
Here, $v_{1i=}$ Speed of particle before collision $=v_0$
$v_{2i}=$ Speed of wall before collision $=-V$
$v_{2f}=$ Speed of wall after collision $=-V$
$v_{1f}=$ Speed of particle after collision $=-v^{\prime }$

Assume after the collision, particle will move in leftward direction.
Hence, $1=\frac{-v-(-v^{\prime })}{v_0-(-v)}$
$v_o+v=-v+v^{\prime }$
$v^{\prime }=2v+v_0$
$v^{\prime }=2\times 5+20$
$v^{\prime }=30\text{m/s}$

Therefore, speed of the particle after collision is $v^{\prime }=30\text{m/s}$ towards left.