You are the ground-control commander of a 2000 kg scientific rocket that is appr

Question

You are the ground-control commander of a 2000 kg scientific rocket that is approaching Mars at a speed of 25,000 km/hr. I needs to quickly slow to 15,000 km/hr. to begin a controlled descent to the surface. If the rocket enters the Martian atmosphere too fast it will burn 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 breaking 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 1390000 m/s relative to the rocket. You need to send the rocket an instruction to tell how many bullets to fire. Success will bring you fame and glory, but failure of this $500,000,000 mission will ruin your career. How many bullets?

Explanation / Answer

The mass of rocket, m = 2000 kg The velocity of rocket at approaching mars = 25000 km/hr = 6944.4 m/s The finla velocity = 15000 m/s = 4166.7 m/s Change in momentum of space craft, p = mass * change in velocity                    p = 2000 ( 6944.4 - 4166.7) = 5.6 * 10^6 kgm/s The mass of bullet, m = 5 kg The speed of bullet, v = 1390000 m/s The momentum of bullet, P = mv = 6.9 * 10^6 m/s Number of bullets, n = P/P = 0.8 bullets

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