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The 'e' Equation

If a ball str...

Question

If a ball strikes with a velocity $u_{1}$ at the wall which itself is approaching it with velocity $u_{2}$ , then find the velocity of the ball after collision with the wall.

ν_{1} = - (u_{2} + 2 u_{2})

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ν_{1} = - (u_{1} + 3 u_{2})

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ν_{1} = - (u_{1} + 4 u_{2})

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ν_{1} = - (u_{1} + 2 u_{2})

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Solution

The correct option is D $ν_{1} = - (u_{1} + 2 u_{2})$
D. $v_{1} = - (u_{1} + 2 u_{2})$

As the wall is heavy so after the collision it will continue to move with the same velocity $u_{2}$ .

The relative velocity of separation is equal to the relative velocity approach.

Hence,

$v_{1} - v_{2} = e (u_{1} - u_{2})$ , where $e =$ coefficient of restitution

In case of perfectly elastic collision

$e = 1$

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

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