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A convex, rearview mirror of focal length 20 cm , is fitted in a car. A 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 - 1 , then the speed of the image of the second car with respect to the first car is

Options

  1. A0.016   m   s - 1
  2. B0.0257   m   s - 1
  3. C0.162   m   s - 1
  4. D0.0073   m   s - 1

Correct answer

A. 0.016   m   s - 1

Step-by-step solution

Mirror formula 1 v + 1 u = 1 f Differentiating w.r.t. t , 0 = - 1 v 2 dv dt - 1 u 2 du dt dv dt = - v 2 u 2 du dt But du dt = 15 m/s Now 1 v = ( 1 20 + 1 600 ) ∴ v = 600 31   cm and v u = 600/31 600 = 1 31 Speed of image = d v dt = - ( 1 31 ) 2 × 15 = 0.016   m / s

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