Answer:
[tex]a_2=-0.00252\ m/s^2[/tex]
Explanation:
Given that,
Mass of the astronaut, m = 70 kg
Mass of the spacecraft, [tex]m'=10^4\ kg[/tex]
Acceleration of the astronaut, [tex]a_1=0.36\ m/s^2[/tex]
To find,
The magnitude of the acceleration of the spacecraft.
Solution,
The force acting on the astronaut is given by :
[tex]F=m\times a_1[/tex]
[tex]F=70\ kg\times 0.36\ m/s^2=25.2\ N[/tex]
During the push, the astronaut accelerates as a result a reaction force will also act on the spacecraft. Let [tex]a_2[/tex] is the acceleration of the spacecraft. It can be calculated as :
[tex]a_2=\dfrac{-F}{m}[/tex] (reaction force)
[tex]a_2=\dfrac{-25.2}{10^4}[/tex]
[tex]a_2=-0.00252\ m/s^2[/tex]
Therefore, the magnitude of the acceleration of the spacecraft is [tex]0.00252\ m/s^2[/tex]. Hence, this is the required solution.
