A gun of mass M fires a bullet of mass m 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.

Explanation

At the time of firing MV'=MV

Consider at time `t=t, `
`u=-(Vt+V't)`
f=-f`
Then, v=?`
Using mirror formula
`1/v+1/u=1/f`
`rarr 1/v+1/f-1/u=-1/f+1/((Vt+V't))`
`=(-(Vt+V't)+f)/((Vt+V't)f)`
`rarr v=(-(V+V')tf)(f-(V+V')t)`
so separatio between imge and bullet at time t
`(-V+V')tf)/(f=(V+V')t)+(V+V')t`
`=(V+V')t[f/(f-(V+V')t)+1]`
`=2(1+m/N)Vt`
Differenciating w.r.t 't'
(d(v-u)/(dt)=2(1+m/M)V`
Hence speed of separation of the bullt and image =2(1+m/M)V.`