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

Question

You are the ground-control commander of a 2000 kg scientific rocket that isapproaching Mars at a speed of 3000 km/hr. It needs to quickly slowto 16000 km/hr to begin a controlled descentto the surface. If the rocket enters the Martian atmosphere toofast it will burn up, and if it enters too slowly, it will use upits maneuvering fuel before reaching the surface and will crash.The rocket has a new braking system: Several 5.0 kg bullets on the frontof the rocket can be fired straight ahead. Each has ahigh-explosive charge that fires it at a speed of111,000 m/s relative to therocket. You need to send the rocket an instruction to tell ithow 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

First convert km/h to m/s:
(2.6*10^4km/h)*(1h/3600s)*(10^3m/km) = 7222.22 m/s
(2.0*10^4km/h)*(1h/3600s)*(10^3m/km) = 5555.56 m/s

Then we apply conservation of momentum:
Vi*m(total) = V2*m2 + Vf*m1

m1 = mass of ship = 2000kg
Vi = initial velocity = 7222.22m/s
m(total) = 5kg

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