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 300 m/s rebounds from the sail at 100 m/s . The design objective is for the cart to reach a speed of 16.0 m/s in 30.0 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

momentum imparted by 1 bullet = m*(vf - vi)
= 0.02 Kg * (100 - (-300)) m/s
= 8 Kgm/s

Let the number of bullet fired in 30 s be n

So total momentum imparted by all bullets= n*8 Kgm/s

Momentum change required for vehicle = 200*16 = 3200 Kgm/s

equate both:
n*8 = 3200
n= 400

number of bullets per second = 400/30 = 13.33

Answer: 13.33 bullet per second

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