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 3.0×10^4 km/hr . It needs to quickly slow to 1.8×10^4 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 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 111,000 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 ruin your career.

Explanation / Answer

mR=2000kg, vo=3.0(104)(km/hr)(1hr/3600s)(1000m/1km)=8.333(103)(m/s), vf=1.8(104)(km/hr)(1hr/3600s)(1000m/1km)=5.000(103)(m/s), mb=5.0kg, vb=1.11(105)(m/s). Initial momentum is: mRvo Final momentum is: mRvf+N(mbvb) since P=0, Po=Pf mRvo=mRvf+N(mbvb) :solve the equation for N, the number of bullets:

mRvo-mRvf=N(mbvb) => ((mR)(vo-vf))/(mbvb)=N :plug in the numbers: ((2000)(8.333(103)-5.000(103))/((5)(1.11(105)))=12=N. so the rocket needs to fire 12 bullets in order for your career not to be ruined(:

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