Astronaut pushing satellite in space shuttle problem

[court2011]

Homework Statement

A 93 kg astronaut and a 1500 kg satellite are at rest relative to the space shuttle. The astronaut pushes on the satellite, giving it a speed of 0.16 m/s directly away from the shuttle. Seven-and-a-half seconds later the astronaut comes into contact with the shuttle. What was the initial distance from the shuttle to the astronaut?

Homework Equations

$$\sum$$F= $$\Delta$$p/$$\Delta$$t

The Attempt at a Solution

 

[XanziBar]

You can use the conservation of momentum Pi=Pf when there are no external forces to find the velocity of the astronaut. Then use speed=distance/time to find the distance.