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 between the sphere and the wall is e = 1/2. The velocity vector of the sphere after it hits the wall is

Moderate

A

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

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

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

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

Solution

$\hat{j}$ component, i.e., component of velocity parallel to wall remains unchanged while $\hat{i}$ component will become (-1/2) $(2 \hat{i}) o r - \hat{i}$ . Therefore, velocity vector of the sphere after it hits the wall is $- \hat{i} + 2 \hat{j}$

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