A 7310 kg space probe, moving nose-first toward Jupiter at 88.3 m/s relative to the Sun, fires its rocket engine, ejecting 54.0 kg of exhaust at a speed of 246 m/s relative to the space probe. What is the final velocity of the probe

Final velocity of Probe; V_f = 656.314 m/s

Explanation:

We are given;

Mass of space probe; m_i = 7310 kg

Initial velocity of probe ; v_i = 88.3 m/s

Mass of exhaust fuel; m = 54 kg

V_rel = 246 m/s

Mass of fuel; m_f = m_i - m = 7310 kg - 54kg = 7256 kg

From Rocket equation;

V_f - V_i = V_rel[In(m_i/m_f)]

Where V_f is final velocity of probe.

Thus, plugging in the relevant values to get ;

V_f - 88.3 = 246[In(7310/7256)]

V_f - 88.3 = 246 x 2.309

V_f - 88.3 = 568.014

Thus, V_f = 568.014 + 88.3 = 656.314 m/s

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