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A ball is approaching a convex mirror of focal length 30 cm with speed 20 m/s. What is the speed of its image when the ball is at 5 m from the mirror?

A ball is approaching a convex mirror of focal length 30 cm with speed 20 m/s. What is the speed of its image when the ball is at 5 m from the mirror?

Grade:12

1 Answers

Arun
25763 Points
2 years ago

We know,

1/f = 1/v + 1/u

=> 1/v = 1/f – 1/u

=> 1/v = (u – f)/(uf)

=> v = uf/(u – f)

Now,

dv/dt = [f/(u – f)]du/dt + uf(-1)(u – f)-2du/dt

=> dv/dt = (du/dt)[{f(u – f) – uf}/(u – f)2]

=> dv/dt = -(du/dt)[(f2)/(u – f)2]

A/Q,

Object distance is, u = -5 m

Object’s speed of approaching, du/dt = -20 m/s

Focal length, f = 30 cm = -0.3 m

So,

dv/dt = -(-20)[(0.32)/(-20 + 0.3)2]

=> dv/dt = 0.0046 m/s

=> dv/dt = 4.6 mm/s

This is the speed of the image.

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