Velocity after slingshot at Jupiter

[suspenc3]

Spacecraft voyager 2 (of mass $$m$$ and speed $$v$$ relative to the sun) approaches the planet Jupiter (of mass $$M$$ and speed $$v_J$$ relative to the sun). The spacecraft rounds the planet and departs in the opposite direction. What is its speed, relative to the sun, after this slingshot encounter, which can be anylized as a collision? Assumer $$v = 12km/s$$ and $$v_J = 13km/s$$ (the orbital speed of jupiter). The mass of Jupiter is very much grater than the mass of the spacecraft .

Can someone point me in the right direction?

Thanks

 

[mezarashi]

Remove the fancy terminology and focus on collision mechanics.

Apply the conservation of momentum equation.
Apply conservation of kinetic energy.

Replace M as a function of m, such that all the m's in the momentum equation cancel. Do some factoring and cancelling and you can make the approximation that $$V_J(final) + V_J(initial) \approx 2V_J(initial)$$ since the mass is very very large compared to the space craft.