Question

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

Answer 1

Final velocity of Probe; V_f = 656.314 m/s

Step-by-step 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

Answer 2

`v_(1f) = 90.12m/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

`7310 * 88.3 = (7310- 54)v_(1f) + 54(v_(1f) - 246)`

`645473 = 7310* v_(1f) - 13284\\658757 = 7310 * v_(1f)`

so we have,

`v_(1f) = 90.12m/s`