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 ${\text{v}}_{\text{i}}={\text{v}}_0$