Problem 9.74 You are the ground-control commander of a 2000 kg scientific rocket

Question

Problem 9.74 You are the ground-control commander of a 2000 kg scientific rocket that is approaching Mars at a speed of 25,000 km/h. It needs to quickly slow to 15,000 km/h to begin a controlled descent to the surface. If the rocket enters the Martian atmosphere too fast it will bum up, and if it enters too slowly, it will use up its maneuvering fuel before reaching the surface and will crash. The rocket has a new braking system: Several 5.0 kg bullets on the front of the rocket can be fired straight ahead. Each has a high-explosive charge that fires it at a speed of 139,000 m/s relative to the rocket. You need to send the rocket an instruction to tell it how many bullets to fire. Success will bring you fame and glory, but failure of this $500,000,000 mission will win your career. Part A How many bullets will you tell the rocket to fire? Express your answer as an integer.

Explanation / Answer

mass of rocket = m1 = 2000 kg

initial speed = u1 = 25000 km/h = 6944.44 m/s

final speed = v1 = 15000 km/h = 4166.66 m/s

mass of bullet = m2 = 5 kg

speed of bullet = v2 = 139000 m/s

Conservation of momentum

m1 u1 = m1 v1 + N m2 v2

N = ( m1 u1 - m1 v1 ) / ( m2 v2 )

N = ( 2000*6944.44 - 2000*4166.66 ) / ( 5*139000 ) = 7.99 = 8

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Number of bullets to be fired = N = 8

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