A 115 kg astronaut and a 970 kg satellite are at rest relative to the space shuttle.?

Question

A 115 kg astronaut and a 970 kg satellite are at rest relative to the space shuttle. The astronaut pushes on the satellite, giving it a speed of 0.18 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?
m

Answer 1

Let's compute the speed of the astronaut using conservation of momentum
0=115*v-970*0.18
solve for v
v=1.52 m/s

the equation of motion is
s(t)=1.52*t
solve for s(7.5)
11.39 m

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