Physics help please on elastic collision! I dont feel like i have enough information!

In space, an elastic 'sling shot' collision is arranged between a 6.4×10 ^24
kg planet moving at 9.0kms ^−1
towards a 6000kg spacecraft which is also moving at 4.5kms ^−1
towards the planet.
Calculate the final speed of the spacecraft.

Hint 3 in isaac is about using momentum and energy, so you have two unknowns and two equations so everything should be good.

Hmmm, so I assume we have to find the momentum before and after, the energy before and after and then use simultaneous equations? Can I also just ask that would i use 9000 in my equation instead of 9km as the usual convention is to use m.

If youve come across it, if energy is conserved (it is here) then restitution = 1 and the difference in velocities before is equal to the difference in velociites after (it just simplifies the energy conservation calculation). Then combine with momentum conservation.

i got 22500 ms^-1 and to 2sf (23000ms^-1). I did Us - Up = Vp - Vs
then assume Vp is Up because of the negligible momentum from the Us. So Vs = Us - 2Up which is 4500 + 18000 to get 22500ms^-1.
Is this the method you were talking about?