A machine gun directs a flow of bullets at a steel target mounted on a cart with negligible friction and of mass 600 kg. In this case, the gun is an Uzi, which uses 9-mm (8.0-g) bullets and can fire at a rate of 10 rounds/s, and the bullets have an average muzzle velocity of 400 m/s. 

(a) Assuming each bullet’s ricochet off the target can be approximated by an elastic collision, with what final velocity would the cart be moving if all 50 rounds in the Uzi’s magazine were fired at the maximum rate at the target? 

(b) How fast would the cart be moving if the target were made of soft wood such that all 50 bullets became embedded? 

(c) The Uzi is now firmly attached to the cart while at rest. The trigger is then pulled, and all 50 rounds are discharged horizontally into the air. What is the final speed of the cart?