A thief is running away in his car with a velocity of 20m/s.A police jeep is following him which is sighted by the thief in his rearview mirror, a convex mirror of focal length 10m.He observes that the jeep is moving towards him with a speed of 1cm/s.If the magnification of the mirror for the jeep at that time is 1/10. Find:

1. actual speed of the jeep

2. rate at which magnification is changing

Question

A thief is running away in his car with a velocity of 20m/s.A police jeep is following him which is sighted by the thief in his rearview mirror, a convex mirror of focal length 10m.He observes that the jeep is moving towards him with a speed of 1cm/s.If the magnification of the mirror for the jeep at that time is 1/10. Find:

1. actual speed of the jeep

2. rate at which magnification is changing

Vikas TU · Answer

Hiii rom the mirror formula 1/v +1/u = 1/f We get the velocity of image as : Vi = m^2 * Vo Vo = Relative velocity of object with respect to mirror Vi = Relative velocity of image m = Linear magnification. Vo = v – 20 Vi = 1cm/sec m = 1/10 Put the value in equation above. v = 21m/sec By the mirror formula we can write as 1/m = (u-f)/f m = f/(u-f) dm/dt = -f/(u-f) 2 . du/dt put value of m and find u u = -90m put the value of u in differential equation. dm/dt = 0.001 per second.

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