Question

A field gun of mass 1.5 tones, fires a shell of mass 15 kg with a velocity of 150m/s. Calculate the velocity of the recoil of the gun.

Answer 1

Mass of gun(M¹)=1.5tonnes
Also 1 tonnes=1000kg
:.M¹=1.5×1000=1500kg
Initial velocity of gun(U¹)=0m s^-1
Final velocity of gun (V¹)=?
Mass of shell(M²)=15kg
Initial velocity of shell (U²)=150m s^-1
Final velocity of shell (V²)=0m s^-1
Now, according to LAW OF CONSERVATION OF MOMENTUM
M¹V¹+M²V²=M¹U¹+M²U²
:. Putting value
(1500×V¹)+(15×0)=(1500×0)+(15×150)
→1500V¹=2250
→V¹=2250/1500
→V¹=1.5m s^-1
:.the velocity of the recoil of the gun is 1.5m s^-1