## Book: HC Verma - Concepts of Physics Part 1

### Chapter: 18. Geometrical Optics

#### Subject: Physics - Class 10th

##### Q. No. 76 of Exercises

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76
##### A gun of mass M fires a bullet of mass with a horizontal speed V. The gun is fitted with a concave mirror of focal length f facing towards the receding bullet. Find the speed of separation of the bullet and the image just after the gun was fired.

the focal length of the concave mirror = f

Mass of the gun= M

Horizontal speed of the bullet= V

Let the recoil speed of the gun= Vg

Using conservation of linear momentum,

At time t= t

The object distance from the mirror, u= -(Vt-t)

Focal length, f= -f

Image distance from the lens, v=?

By using mirror formula,

The separation between the image of bullet and the bullet at time t I given by

Differentiating the equation with respect to t, we get

Therefore, the speed of separation of the bullet and image just after the gun was fired is

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