What Is Voyager 2's Speed After Jupiter Slingshot?

[Zonda]

Spacecraft Voyager 2 (of mass m and speed v relative to the Sun) approaches the planet Jupiter (of mass M and speed V relative to the Sun) as shown in Fig. 10-60. 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 analyzed as a collision? Assume v = 12 km/s and V = 13 km/s (the orbital speed of Jupiter). The mass of Jupiter is very much greater than the mass of the spacecraft (M >> m).

I don't understand how to solve this problem without numbers for masses.

 

[Andrew Mason]

Spacecraft Voyager 2 (of mass m and speed v relative to the Sun) approaches the planet Jupiter (of mass M and speed V relative to the Sun) as shown in Fig. 10-60. 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 analyzed as a collision? Assume v = 12 km/s and V = 13 km/s (the orbital speed of Jupiter). The mass of Jupiter is very much greater than the mass of the spacecraft (M >> m).

I don't understand how to solve this problem without numbers for masses.

I think the idea here is that in its initial position a large distance from Jupiter it has 0 potential with respect to Jupiter and has positive kinetic energy. After its encounter with Jupiter, and its return to its initial position traveling in the opposite direction, what can you say about its total energy? Has there been any change? So what is its kinetic energy/speed?

AM