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Question

An object O is moving with velocity (^i+2^j+3^k) m/s and a plane mirror facing the object is lying in (yz) plane. If the mirror is moving with velocity 2^i m/s, the velocity of image w.r.t object (in SI units) is :

A
^i+2^j+3^k
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B
2^i
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C
3^i+2^j+^k
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D
^i2^j3^k
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Solution

The correct option is B 2^i
For the mirror lying in (yz) plane, the x-axis will represent the normal direction for the mirror.

Therefore, along the normal to mirror :
(vm)x=(vo)x+(vi)x2
2^i=1^i+(vi)x2
(vi)x=(41)^i=3^i m/s

Mirror is lying along (yz) plane, therefore (vi)y and (vi)z will be same as that of object velocity component
(vi)y=2^j, (vi)z=3^k
or, vi=(3^i+2^j+3^k) m/s

Velocity of image w.r.t object,
vi,o=(3^i+2^j+3^k)(^i+2^j+3^k)
vi,o=2^i m/s

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