Question

You fire a rifle of mass 4 kg such that it is free to recoil. The bullet has a mass 28 g and travels horizontally with a speed of 373 m/s relative to the ground. What is the recoil speed (m/s) of the rifle immediately after firing? Don't round during the calculation, keep at least two decimal places.

Answer 1

We will use conservation of linear momentum ( horizontal direction) in this problem as no external horizontal force acts on the rifle-bullet system.

M= mass of rifle; m= mass of bullet and V = velocity of rifle (assumed in + x) ; v= velocity of bullet ( assumed in +x direction)

Before firing the bullet , initial momentum , Pi = 0 (no movement of either rifle or bullet

And after firing, the momentum Pf = MV + mv

from conservation of momentum, Pi = Pf ====> 0 = MV +mv =====> V = -mv/M ==> V = - 2.611 m/s

**The negative sign depicts that the assumed direction of V is opposite to the actual direction, hence the direction of the rifle's velocity will be in negative X direction.