A smooth sphere is moving on a horizontal surface with a velocity vector $\left(2\hat{\mathrm{i}}+2\hat{\mathrm{j}}\right) \mathrm{m} {\mathrm{s}}^{-1}$ immediately before it hits a vertical wall. The wall is parallel to the vector $\widehat{\text{j}}$ and the coefficient of restitution between the sphere and the wall is $e=\frac{1}{2}$. The velocity of the sphere, after it hits the wall, is

• A

  $\widehat{\mathrm{i}}-\widehat{\mathrm{j}}$
• Correct answer
  B

  $-\widehat{\mathrm{i}}+2\widehat{\text{j}}$
• C

  $-\widehat{\mathrm{i}}-\widehat{\mathrm{j}}$
• D

  $2\widehat{\mathrm{i}}-\widehat{\mathrm{j}}$

Solution

$\frac{1}{2}=\frac{0-v_x}{2}$

$v_x=-1$

$\overrightarrow{\mathit{\text{v}}}=-\hat{\text{i}}+2\hat{\text{j}}$

Hence, the correct answer is option: 'B'.