First slide

Line of impact

Question

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

Difficult

A

$\hat{i} - \hat{j}$
B

$- \hat{i} + 2 \hat{j}$
C

$- \hat{i} - \hat{j}$
D

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

Solution

If y axis parallel to the wall. Velocity along y direction will not change.
$\begin{array}{l} e = \frac{- V_{x}}{U_{x}} = \frac{1}{2} \\ v_{x} = \frac{- u_{x}}{2} = \frac{- 2}{2} = - 1 \\ F i n a l v e l o c i t y = - i + 2 j \end{array}$

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