Q76 of 123 Page 412

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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Two concave mirrors of equal radii of curvature R are fixed on a stand facing opposite directions. The whole system has a mass m and is kept on a frictionless horizontal table (figure 18-E15).


Two blocks A and B, each of mass m, are placed on the two sides of the stand. At t = 0, the separation between A and the mirrors is 2R and also the separation between B and the mirrors is 2R. The block B moves towards the mirror at a speed v. All collisions which take place are elastic. Taking the original position of the mirrors-stand system to be x = 0 and X-axis along AB, find the position of the images of A and B at t =



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