Question

A point object is moving with velocity $\text{v}_{0} = 2 \hat{\text{i}} - 3 \hat{\text{j}} + 4 \hat{\text{k}}$ in front of a moving plane mirror whose normal is along x - axis. The mirror is moving with velocity $\text{v}_{\text{m}} = \hat{\text{i}} - 4 \hat{\text{j}} + 2 \hat{\text{k}}$ . Find the velocity vector of image.

• A. $- 5 \, \hat{\text{j}}$
• B. $- 3 \, \hat{\text{j}} + 4 \, \hat{\text{k}}$
• C. $- 4 \, \hat{\text{j}} + 2 \, \hat{\text{k}}$
• D. $2 \, \hat{\text{i}} - 3 \, \hat{\text{j}} + 2 \, \hat{\text{k}}$

Answer 1

Answer: (B)

Let velocity of image $\text{v}_{\text{i}}=\text{x }\hat{\text{i}}+\text{y }\hat{\text{j}}+z\hat{\text{k}}$
Along the normal, i.e., along x-axis.
$\text{v}_{\text{im}} = - \text{v}_{\text{om}}$
$\Rightarrow \left(\text{x}\right) - \left(1\right) = - \left[\left(2\right) - \left(1\right)\right]$
$\Rightarrow \text{x} = 0$
Along y and z - axes $\text{v}_{\text{i}} = \text{v}_{0}$