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Question

# A convex driving mirror of focal length 20 cm, is fitted in a motor car. If the second car 2 m broad and 1.6 m high is 6 m away from the first car and overtakes the first car at a relative speed of 15 m/s, then how fast relatively in m/s will the image be moving? Answer upto 3 decimal places

A
0.017
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B
0.015
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C
0.016
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Solution

## Mirror formula, 1v+1u=1f Differentiating w.r.t t, we get0=−1v2dvdt−1u2dudt or dvdt=−v2u2dudt But dudt=15 m/s Now,1v=120+1600 or v=60031 cm and speed of image =dvdt=(131)2×15=0.016 m/s Why this question? To learn to find the image velocity when the object velocity and its relative position with respect to the mirror is known.

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