Question

A mirror faces the negative x-axis. (Normal to its reflecting surface is$-\hat{i})$ While a particle starts moving such that its image is formed in the mirror. At a certain instant the velocity of the particles is $3\hat{i}+4\hat{j}+5\hat{k}$ and that of the mirror is $\hat{1}-\hat{j}+\hat{k}$ Choose the correct options.

• A. Magnitude of relative velocity of the image w.r.t mirrror is$\sqrt{45}$
• B. Magnitude of relative velocity of image w.r.t object is 4
• C. Magnitude of relative velocity of image w.r.t mirrror is $\sqrt{45}$
• D. Absolute velocity of the image w.r.t ground is$\sqrt{42}$

Answer 1

Answer: (A), (C)

The correct options are
A Magnitude of relative velocity of the image w.r.t mirrror is$\sqrt{45}$
C Magnitude of relative velocity of image w.r.t mirrror is $\sqrt{45}$

$\begin{array}{c}Iny-direction\\ V_o=V_i\\ \Rightarrow V_i=4\hat{j}\\ Inz-direction\\ V_i=V_o\\ \Rightarrow V_i=5\hat{k}\\ Inx-direction\\ V_{IM}=-V_{oM}\\ \Rightarrow V_{IM}=-V_{oM}\\ \Rightarrow V_I-V_M=V_M-V_o\\ \Rightarrow V_I=2V_M-V_o\\ =2\left[\hat{i}\right]-3\left[\hat{i}\right]\\ =-\hat{i}\\ \therefore \overrightarrow{V_I}=-\hat{i}+4\hat{j}+5\hat{k}\\ \therefore \overrightarrow{V_{iM}}=-2\hat{i}+5\hat{j}+4\hat{k}\\ \therefore \left|\overrightarrow{V_{iM}}\right|=\sqrt{45}\end{array}$

Hence,

option $\left(A\right)$ and $\left(C\right)$ are both correct answer.