Question

A certain mirror placed at the origin has $\hat{j}$ as the normal vector to its reflecting surface. The mirror begins to translate with a velocity $\hat{i}+\hat{j}+\hat{k}$ at $t=0$. At the same time an object which was initially at $\hat{i}+\hat{j}$ starts moving with a velocity $(\hat{i}+\hat{j})m/s$ , then which of the following is/are correct ?

• A. initial position of the image will be $\hat{i}-\hat{j}$
• B. The velocity of the image will be $\hat{i}+\hat{j}+2\hat{k}$
• C. The velocity of image relative to the object will be $2\hat{k}$
• D. The velocity of image relative to the mirror will be $\hat{k}$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A initial position of the image will be $\hat{i}-\hat{j}$
B The velocity of the image will be $\hat{i}+\hat{j}+2\hat{k}$
C The velocity of image relative to the mirror will be $\hat{k}$
D The velocity of image relative to the object will be $2\hat{k}$

If the mirror moves with a velocity of V then image of the object moves with the velocity of 2V with the same direction of mirror. If the object moves with a velocity of V then image also moves with same speed but opposite in direction.
a) Initially , the mirror is along x axis and the object is at $\hat{i}+\hat{j}$
Hence , its reflection will be at $\hat{i}-\hat{j}$ as the normal of the mirror is along $\hat{j}$
b) Velocity of image is Twice the velocity of the mirror$-$that of the object = $2(\hat{i}+\hat{j}+\hat{k})-\hat{i}-\hat{j}=\hat{i}+\hat{j}+2\hat{k}$
c) Velocity of image relative to the object is $\hat{i}+\hat{j}+2\hat{k}-\hat{i}-\hat{j}=2\hat{k}$
d) Velocity of the image wrt the mirror is $\hat{i}+\hat{j}+2\hat{k}-(\hat{i}+\hat{j}+\hat{k})=\hat{k}$