A 91-kg astronaut and a 1300-kg satellite are at rest relative to the space shuttle. The astronaut pushes on the satellite, giving it a speed of 0.17 m/s directly away from the shuttle. Seven-and-a-half seconds later the astronaut comes into contact with the shuttle. Required:
What was the initial distance from the shuttle to the astronaut?

18.2145 meters

Explanation:

Using the conservation of momentum, we have that:

m1 = m1' is the mass of the astronaut, m2=m2' is the mass of the satellite, v1 and v2 are the inicial speed of the astronaut and the satellite (v1 = v2 = 0), and v1' and v2' are the final speed of the astronaut and the satellite. Then we have that:

The negative sign of this speed just indicates the direction the astronaut goes, which is the opposite direction of the satellite.

If the astronaut takes 7.5 seconds to come into contact with the shuttle, their initial distance is:

the answer for apex is the lowest

we need to know the time interval during which the force acts. impulse of force = momentum change