Rocket expelling fuel velocity relative to earth

[j3dwards]

Homework Statement

A rocket moving in space, far from all other objects, has a speed of 3.0 × 10³ ms⁻¹ relative to the Earth. Its engines are turned on, and fuel is ejected in a direction opposite to the rocket’s motion at a speed of 5.0 × 10³ ms⁻¹ relative to the rocket. What is the speed of the rocket relative to the Earth once the rocket’s mass is reduced to half its mass before ignition?

Homework Equations

v_fuel = v - v_ex

The Attempt at a Solution

Quite unsure as to how to attempt this. How do I found v_ex in order to find v? It has something to do with the mass but I'm not sure how to relate it.

This question is only worth 2 marks so I don't think I'm expected to show much. Thank you.

 

[Filip Larsen]

This question test if you know about the rocket equation [1].

[1] http://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation

 

[ArmanCham]

You have to use momentum conservation but you need to pick a referance frame.Pick Earth referance frame calculate velocities to Earth,then use momentum conservation

 

[haruspex]

You have to use momentum conservation but you need to pick a referance frame.Pick Earth referance frame calculate velocities to Earth,then use momentum conservation

It's not that simple. The speed of the exhaust in an inertial frame reduces as the rocket accelerates. You need to use (or to derive) the rocket equation Filip mentions.