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The 'e' Equation

A particle of...

Question

A particle of mass $m$ moves with $v_{0} = 20 m / s$ towards a wall that is moving with $v = 5 m / s$ in the opposite direction. If the particle collides with the wall without losing its energy, find the speed of the particle just after the collision.

30 m / s

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40 m / s

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50 m / s

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60 m / s

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Solution

The correct option is A $30 m / s$
A particle of mass m moving with velocity $u_{1}$ moves towards a wall that is moving with velocity $u_{2}$ in the opposite direction, then the velocity of approach ,

$u_{a} = u_{1} + u_{2}$

Let the velocity of the particle just after collision be $v_{1}$ and the velocity of wall is $v_{2}$ ,

the velocity of separation,

$v_{s} = v_{1} - v_{2}$

The coefficient of restitution,

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

As there is no loss of energy, collision is elastic, $e = 1$

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

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

Putting $u_{1} = 20 m / s$ , $u_{2} = 5 m / s$ , $v_{2} = 5 m / s$

$v_{1} = 20 + 5 + 5$

$v_{1} = 30 m / s$

The correct option is A.

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