A smooth sphere is moving on a horizontal surface with velocity vector $2 \bar{i} + 2 \bar{j}$ immediately before it hits a vertical wall. The wall is parallel to $\bar{j}$ vector and the coefficient of restitution between the sphere and the wall is $e = \frac{1}{2}$ . The velocity vector of the sphere after it hits the wall is

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$\bar{i} - \bar{j}$

$- 2 \bar{i} - 2 \bar{j}$

$- \bar{i} + 2 \bar{j}$

$2 \bar{i} - \bar{j}$

answer is A.

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Detailed Solution

$Along wall, velocity is same.$

$Normal to wall \bar{V} = - e \bar{V} = \frac{I}{2} (- 2 \hat{i}) = - \hat{i}$

$Final velocity = - \hat{i} + 2 \hat{j}$

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