The astronaut final velocity is 0.06 m/s to the right
Explanation:
In absence of external forces, the total momentum of the box-astronaut system is conserved.
At the beginnig, the total momentum of the two is zero, since they are at rest:
![p_i = 0](https://tex.z-dn.net/?f=p_i%20%3D%200)
While the final momentum, after the astronaut throws the box, is:
![p_f=mv+MV](https://tex.z-dn.net/?f=p_f%3Dmv%2BMV)
where
m = 11 kg is the mass of the box
M = 79 kg is the mass of the astronaut
v = -0.45 m/s (to the left) is the velocity of the box (we take left as negative direction)
V is the final velocity of the astronaut
The total momentum is conserved, so
![p_i = p_f\\0=mv+MV](https://tex.z-dn.net/?f=p_i%20%3D%20p_f%5C%5C0%3Dmv%2BMV)
And solving , we find V:
![V=-\frac{mv}{M}=-\frac{(11)(-0.45)}{79}=0.06 m/s](https://tex.z-dn.net/?f=V%3D-%5Cfrac%7Bmv%7D%7BM%7D%3D-%5Cfrac%7B%2811%29%28-0.45%29%7D%7B79%7D%3D0.06%20m%2Fs)
And the positive sign indicates that the direction is to the right.
Learn more about momentum:
brainly.com/question/7973509
brainly.com/question/6573742
brainly.com/question/2370982
brainly.com/question/9484203
#LearnwithBrainly