Solving the Spacewalking Astronaut Problem

[turtledove]

Homework Statement

A 68.7 kg spacewalking astronaut pushes off a 653.0 kg satellite, exerting a 153.0 N force for the 0.763 s it takes him to straighten his arms. How far apart are the astronaut and the satellite after 9.36 min?

Homework Equations

d = vit + 1/2 at^2

The Attempt at a Solution

F = ma
153 = (653 + 68.7) a
a = 0.211 m/s^2

d = 0 = 1/2 (0.211)(561.6)^2
= 33203 m

This is incorrect, what am i doing wrong here?

 

[PhanthomJay]

Homework Statement

A 68.7 kg spacewalking astronaut pushes off a 653.0 kg satellite, exerting a 153.0 N force for the 0.763 s it takes him to straighten his arms. How far apart are the astronaut and the satellite after 9.36 min?

Homework Equations

d = vit + 1/2 at^2

The Attempt at a Solution

F = ma
153 = (653 + 68.7) a
a = 0.211 m/s^2

d = 0 = 1/2 (0.211)(561.6)^2
= 33203 m

This is incorrect, what am i doing wrong here?

You are doing a few things wrong. The force is applied to the satellite by the astronaut, and the satellite applies that same force to the astronaut, in the opposite direction, per Newton 3. The acceleration acts only during the first 0.763 seconds, after which there is no longer any force, and thus, no more acceleration, and each move apart at different constant velocities. You might want to try impulse-momentum and conservation of momentum principles.