Question

A bullet of mass 50 gram is fired from a 5 kg gun with a velocity of 1 km per hour the speed of recoil of the gun is

Answer 1

mass of bullet = 50g = 50/1000 kg => 1/20kg
velocity of bullet = 1km/h => 5/18×1 m/s => 5/18 m/s
mass of gun = 5kg
velocity of gun (recoil) => ? (to be determined)

we know that ,
mass of bullet × velocity of bullet = mass of gun × velocity of gun
1/20 × 5/18 = 5 × velocity of gun
1/72 = 5×velocity of gun
1/72 × 1/5 = velocity of gun
1/360 m/s => velocity of gun (recoil)
or we can write, 1/360 × 18/5 => 1/100 km/h
hope this helps

Answer 2

Momentum is conserved.
Initial momentum = Final momentum
0 = m1v1 + m2v2
v2 = -m1v1 / m2
v2 = -(50 * 10^-3 * 5/18)/5
v2 = -0.0027 m/s
v2 = -0.00972 km/h
Recoil of the gun is 0.00972km/h in opposite direction of velocity of bullet.