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Q.

You are sitting inside a parked car and observing the things behind the car in rear view mirror. For this situation mark the correct statement(s) 

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a

A jogger approaching your car at constant velocity (with respect to ground) appears to you to run with decreasing velocity. 

b

A jogger approaching your car at constant velocity (with respect to ground) appears to you to run with increasing velocity

c

A jogger approaching your car with decreasing velocity at constant rate may appear to you to move with constant velocity. 

d

A jogger approaching your car with decreasing velocity at variable rate may appear to you to move with constant velocily.

answer is A, D.

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Detailed Solution

Question Image

The rear view mirror of the car is of convex type. From mirror formula

1v+1u=1f

1v2dvdt1u2dudt=0dvdt=v2u2dudt

vi=v2u2×v0  where dvdt is velocity of image with respect to mirror, as mirror is at rest it can be considered as velocity of image with respect to ground and similarly dudt is velocity of object with respect to ground. From 1v+1u=1f

1v=1f1u=ufuf=vu=fuf

As object (here jogger) approaches mirror (car) the value of u decreases. Here u is negative and f is positive, So uf would be negative.

As jogger approaches mirror with constant velocity the value of u decreases and hence uf decreases and hence vu increases. So V1 increases, hence a is correct V1 would be constant if vu2×v0 is constant

which may be possible for situation of option (4).

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