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Moving Mirror

What is the v...

Question

What is the velocity (in cm/s) of image in situation shown below? Object moves with velocity 10 cm/s and mirror moves with velocity 2 cm/s as shown.

A

2 cm/s

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B

0 cm/s

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C

4 cm/s

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D

1 cm/s

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Solution

The correct option is B 0 cm/s
In the mirror frame of reference,

$v_{0} = 8 c m / s$
$v_{i} = - {(\frac{v}{u})}^{2} v_{0}$
$= - {(\frac{f}{f - u})}^{2} v_{0} = - (\frac{10}{10 + 10})^{2} \times v_{0}$
$= - (\frac{1}{4}) \times 8$
$= - 2 c m / s$

So with respect to ground, speed of image

$v_{i}^{'} = - 2 + 2 = 0 c m / s$

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