A projectile with mass of 10 grams is shot from a rifle with mass of 5 kg.
The velocity of the projectile a moment after shooting from the barrel is 200 m/s. Calculate the velocity of the rifle's jerking motion at the moment the projectile shoots from the rifle.
Solution
mₚ = 10 grams = 0.01 kg; mₛ = 5 kg
vₚ = 200 m/s
Use the law of conservation of momentum. Before the projectile shoots, vₚ and vₛ are zero.
mₚvₚ + mₛvₛ = mₚvₚ' + mₛvₛ'
0 + 0 = (0.01)(200) + (4.99)vₛ'
0 = 2 + 4.99vₛ'
-2 = 4.99vₛ'
vs' = –0.4 m/s
So, the velocity of the rifle's jerking motion is 0.4 m/s backwards.