The Army of the Nation of Whynot has a plan to propel small vehicles across the

Question

The Army of the Nation of Whynot has a plan to propel small vehicles across the battlefield by shooting them, from behind, with a machine gun. They've hired you as a consultant to help with an upcoming test. A 200 kg test vehicle will roll along frictionless rails. The vehicle has a tall "sail" made of ultrahard steel. Previous tests have shown that a 20.0 g bullet traveling at 400 m/s rebounds from the sail at 200 m/s . The design objective is for the cart to reach a speed of 11.0 m/s in 20.0 s . You need to tell them how many bullets to fire per second from the machine gun. Note that your answer should be a rate, which can be fractional, rather than a quantity, which must be an integer.

Explanation / Answer

The kinetic energy we needed is

KE1 =(1/2)mv2 =0.5*200*(11)2 =12100J

and now the bullet tranfers half their energy

KE2 =(1/2)20*10-3*(200)2 =400J

Now dividing KE1/KE2 12100/400 =30.25

We need 30.25 almost 30 bullets in 20s to fire from the gun per second from the machine gun

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