Question

An object and a plane mirror are moving as shown in figure. Determine the velocity of image with respect to ground.

• A. $4\hat{i}+3\hat{j}\text{m/s}$
• B. $-4\hat{i}\text{m/s}$
• C. $-4\hat{i}+3\hat{j}\text{m/s}$
• D. $4\hat{i}\text{m/s}$

Answer 1

The correct option is D $4\hat{i}\text{m/s}$

Given:

Velocity of object with respect to ground along $\text{x-axis}$, $V_{Ox}=4\text{m/s}$

Mirror's velocity with respect to ground, along $\text{x-axis}$, $V_{mx}=5\cos {37}^{\circ }=+4\text{m/s}$, and

Mirror's velocity with respect to ground, along $\text{y-axis}$,
$V_{my}=5\sin {37}^{\circ }=+3\text{m/s}$

Let the image's velocity with respect to ground be $V_I$.

Velocity of object with respect to mirror along $\text{x-axis}$ is given by

$V_{Omx}=V_{Ox}-V_{mx}=4-4=0$

Similarly, velocity of object with respect to mirror along $\text{y-axis}$ is given by

$V_{Omy}=V_{Oy}-V_{m_y}=0-3=-3\text{m/s}$

Velocity of image w.r.t mirror along $\text{x-axis}$ is given as,

$V_{Imx}=-V_{Omx}$

$\therefore V_{Imx}=0\text{m/s}$

Similarly, velocity of image w.r.t mirror along $\text{y-axis}$ is given as,

$V_{Imy}=V_{Omy}$

$\therefore V_{Imy}=-3\text{m/s}$

Lets the velocity of image with respect to ground along$\text{x-axis}$ and $\text{y-axis}$ are $V_{Ix}$ and $V_{Iy}$ respectively.

Using the concept of relative velocity,

$V_{Imx}=V_{Ix}-V_{mx}$

$\Rightarrow V_{Ix}=V_{Imx}+V_{mx}=0+4=4\text{m/s}$

Similarly,

$V_{Iy}=V_{Imy}+V_{my}=-3+3=0\text{m/s}$

$\therefore V_I=V_{Ix}\hat{i}+V_{Iy}\hat{j}=4\hat{i}\text{m/s}$

Hence, correct option is (d).

$\begin{array}{c}AnsD\end{array}$