A loaded gun is dropped on a frozen lake. The gun fires, with the bullet going horizontally in one direction and the gun sliding on the ice in the oth

Question

A loaded gun is dropped on a frozen lake. The gun fires, with the bullet going horizontally in one direction and the gun sliding on the ice in the other direction. The bullet's mass is 0.03 kg, and its speed is 285 m/s. If the gun's mass is 2.3 kg, what is its speed (in m/s)?

Answer 1

Conservation of momentum

Before firing momentum of system = 0 (constant)

If bullet fires east assume positive direction east

Then if v is speed of gun, momentum of system after firing

to east : 0.03 x 285

to west : 2.3 v (which is -2.3v to east)

So total momentum to east = 0.03 x 285 - 2.3v = 0

So you can calculate v from this