Question

A shell of mass .02 Kg is fired by a gun of mass 100 Kg. If the muzzle speed of the shell is 80m/s-1, what is the recoil velocity of the gun?​

Answer 1

Tips:-

Let the mass of the the bullet be m

Let the mass of the gun be n

let the muzzle velocity be u i.e.80 m/s²

as we all know the gun and the bullet were at rest before the action.

So, the initial speed of both the objects should be 0.

Answer:-

mu+np= mv + nq

where u and p are the initial velocity of the bullet and gun respectively.

and v and q are the final velocity of bullet and gun respectively.

As we know the initial velocities are supposed to be 0, thus the LHS is 0.

$0 = 0.2 \times 80 + 100 \times q \\ \implies16 = - 100q \\ \implies \: q = - 0.16$

Therefore, the gun would recoil with a velocity of 0.16m/s².

Hope it helps

^_^