Question

A ball of mass $10\text{kg}$ initially at rest starts moving under the influence of a constant force $50\text{N}$. Ball covers $10\text{m}$ before colliding a heavy wall which is moving towards the ball with speed $10\text{m/s}$ as shown in figure. If force stops acting on ball just before collision and collision is perfectly elastic, find the velocity of ball after collision.

• A. $0\text{m/s}$
• B. $10\text{m/s}$
• C. $20\text{m/s}$
• D. $30\text{m/s}$

Answer 1

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

Given, $F=50\text{N},m=10\text{kg}$
$a=F/m=50/10=5{\text{m/s}}^2$
Speed of ball just before collision is $u^{\prime }$,
$(u^{\prime }{)}^2=u^2+2as(u=0\because \text{ball is initially at rest})$
$\Rightarrow (u^{\prime }{)}^2=2\times 5\times 10$
$\therefore \left(u^{\prime }\right)=10\text{m/s}$
Just before collision

Wall is very heavy and collision is elastic, therefore velocity of wall will not change even after collision.
Velocity of seperation = velocity of approach
$v-10=10+10$
$\Rightarrow v=30\text{m/s}$