Question

A 5510 kg space probe, moving nose-first toward Jupiter at 250 m/s relative to the Sun, fires its rocket engine, ejecting 75.0 kg of exhaust at a speed of 241 m/s relative to the space probe. What is the final velocity of the probe

Answer 1

final velocity of the probe 253.30 m/s

Step-by-step explanation:

Mass of space probe mi= 5510 kg

initial speed of probe vi= 250 m/s

Exhaust mass m= 75 kg

speed of exhaust vf = 241 m/s

Mass of the fuel mf= mi-m = 5510-75 =5435 kg

Final speed of probe

`v_(f)=v_(i)+v_(r)ln((m_(i))/(m_(f)) )\\v_(f)=250+241 * ln((5510)/(5435) \\v_(f)=250+3.30\\v_(f)=253.30 m/s`

final velocity of the probe 253.30 m/s