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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

 

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

Grade:11

1 Answers

Vikas TU
14149 Points
2 years ago
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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