Question

. A thief is running away in a car with velocity of 20
m/s. A police jeep is following him, which is sighted
by thief in his rear view mirror which is a convex
mirror of focal length 10 m. He observes that the
image of jeep is moving towards him with a velocity
of 1 cm/s. If the magnification of the mirror for the
jeep at that time is 1/10. Find
ay actual speed of jeep
on
(b) rate at which magnification is changing
Assume that police jeep is on axis of the mirror.​

Answer 1

Answer:

Explanation:

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

First we need to consider magnification of mirror which is given as 1/10 and since police jeep will be behind consider u = - x and the virtual image will be 1/10 times so it will be x/10.

Now since focal length is convex f = + 10

By using mirror formula we get

10/x – 1/x = 1/10

9/x = 1/10

So x = 90 m  

Now image velocity is 1 cm/sec, we need to find actual speed on g.

We know that object speed is v1 and image speed is m^2v1 and m = 1/10

                                                                        = (1/10)^2 x v1

                                                                       = 1/100 v1

                                         So v1 = 100 cm/sec

                                              V1 = 1m/sec

Now the jeep is 1m/s behind and speed of thief is 20 m/s

So adding 20 + 1 = 21 m/s is the actual speed of jeep.

Now rate at which magnification is changing will be dm/dt = -f / (u – f)^2 = du / dt = 10 ^-3 / sec