A70.0-kg astronaut pushes to the left on a spacecraft with a force f in "gravity-free" space. the spacecraft has a total mass of 1.0 x 10^4 kg. during the push, the astronaut accelerates to the right with an acceleration of 0.36 m/s^2. determine the magnitude of the acceleration of the spacecraft.

Explanation:

Given that,

Mass of the astronaut, m = 70 kg

Mass of the spacecraft,

Acceleration of the astronaut,

To find,

The magnitude of the acceleration of the spacecraft.

Solution,

The force acting on the astronaut is given by :

During the push, the astronaut accelerates as a result a reaction force will also act on the spacecraft. Let is the acceleration of the spacecraft. It can be calculated as :

(reaction force)

Therefore, the magnitude of the acceleration of the spacecraft is . Hence, this is the required solution.