Answer
The spacecraft’s final speed is about 29.6 km/s.
Work Step by Step
The interaction between the planet and Saturn is an elastic collision, because gravity is a conservative force.
Treat this like a one-dimensional collision, with A being the spacecraft and B being Saturn.
Use equation 7–7 for head-on elastic collisions, and solve for the spacecraft’s final velocity.
$$v_A-v_B=-(v’_A-v’_B)$$
We may assume that Saturn’s velocity is unchanged by the collision.
$$10.4km/s-(-9.6km/s)=-(v’_A-(-9.6km/s))$$
$$ v’_A =-29.6km/s$$
The spacecraft’s final speed is about 29.6 km/s.
