A space probe with a mass of 5060 kg is moving nose-first toward Jupiter at a speed of 208 m/s relative to the Sun. It fires its rocket engine, ejecting 140 kg of exhaust at a speed of 292 m/s relative to the space probe.

What is the final velocity of the probe?

Question

13-03-2024
Physics

College

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A space probe with a mass of 5060 kg is moving nose-first toward Jupiter at a speed of 208 m/s relative to the Sun. It fires its rocket engine, ejecting 140 kg of exhaust at a speed of 292 m/s relative to the space probe.

What is the final velocity of the probe?

Answer :

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xrichi979 xrichi979 · Answer 1 · 2024-12-10T04:16:02-05:00

Final answer:

The final velocity of the space probe, moving toward Jupiter, can be found using the principle of conservation of momentum. The equation (5060 kg * 208 m/s) - (140 kg * 292 m/s) = 5060 kg * v_f, solved for v_f, would give the final velocity.

Explanation:

This problem can be solved using the principle of conservation of momentum. In this case, the momentum before the rocket engine is fired equals the momentum afterwards.

The total momentum before the engine is fired is the mass of the space probe times its velocity relative to the Sun (5060 kg * 208 m/s).

When the rocket engine fires, both the space probe and the exhaust have momentum. The exhaust is ejected with a momentum of 140 kg * 292 m/s. The final momentum of the space probe is therefore the initial momentum minus the momentum of the ejected exhaust.

Using these relationships, you can set up an equation and solve for the final velocity of the space probe, v_f.

(5060 kg * 208 m/s) - (140 kg * 292 m/s) = 5060 kg * v_f

Then, you solve for v_f to find the final velocity of the probe.

Learn more about Conservation of Momentum here:

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A space probe with a mass of 5060 kg is moving nose-first toward Jupiter at a speed of 208 m/s relative to the Sun. It fires its rocket engine, ejecting 140 kg of exhaust at a speed of 292 m/s relative to the space probe. What is the final velocity of the probe?

Answer :

Final answer:

Explanation:

Learn more about Conservation of Momentum here:

Other Questions

A space probe with a mass of 5060 kg is moving nose-first toward Jupiter at a speed of 208 m/s relative to the Sun. It fires its rocket engine, ejecting 140 kg of exhaust at a speed of 292 m/s relative to the space probe.

What is the final velocity of the probe?