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

Answer:

final velocity of the probe 253.30 m/s

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

$v_{f}=v_{i}+v_{r}ln(\frac{m_{i}}{m_{f}} )\\v_{f}=250+241 \times ln(\frac{5510}{5435} \\v_{f}=250+3.30\\v_{f}=253.30 m/s$

final velocity of the probe 253.30 m/s