Question

A gun of mass m1 fires a bullet of mass m2 with a horizontal speed vo(object) . the gun is fitted with a concave mirror of focal length 'f' facing towards the receding bullet. find the seperation of the bullet and it's image?​

Answer 1

here is your answer.

❤❤❤❤❤❤❤❤

mahi the beautiful

Given,

The focal length of the concave mirror is f and M is the mass of the gun. Horizontal speed of the bullet is V.

Let the recoil speed of the gun be Vg

Using the conservation of linear momentum we can write,

MVg = mV

⇒Vg=mMV

Considering the position of gun and bullet at time t = t,

For the mirror, object distance, u = − (Vt + Vgt)

Focal length, f = − f

Image distance, v = ?

Using Mirror formula, we have:

1v+1u=1f⇒ 1v=1−f−1u⇒1v=−1f+1(Vt+Vgt)⇒1v=−(Vt+Vgt)+f(Vt+Vgt)f⇒ v=−(V+Vg)tff−(V+Vg)t

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

v−u=−(V+Vg)tff−(V+Vg)t+(V+Vg)t=(V+Vg) t [ff−(V+Vg)t+1]=2(1+mM)Vt

Differentiating the above equation with respect to 't' we get,

d(v−u)dt=2(1+mM)V

Therefore, the speed of separation of the bullet and image just after the gun was fired is 2(1+mM)V.