Question

A 6000 kg space probe moving nose-first toward Jupiter at 100 m/s relative to the Sun fires its rocket engine, ejecting 80.0 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

`v_(1f) = 103.2 m/s`

Step-by-step explanation:

As we know that Probe along with rocket system is an isolated system

So here net force on this system must be zero

and we can use momentum conservation for this system

So we will have

`(m_1 + m_2)v_(i) = m_1v_(1f) + m_2v_(2f)`

here we know that

`6000 * 100 = (6000- 80)v_(1f) + 80(v_(1f) - 241)`

`6 * 10^5 = 6000* v_(1f) - 19280`

`6.19 * 10^5 = 6000 * v_(1f)`

so we have

`v_(1f) = 103.2 m/s`