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Answer :
Final answer:
205 kg is the astronaut's velocity increases after throwing the ball, necessitating accounting for both her mass and the ball's mass in the final total. So the correct option is Option C) 205 kg.
Explanation:
When the astronaut throws the ball, according to Newton's third law of motion, for every action, there is an equal and opposite reaction. As the astronaut throws the ball with a velocity of 20 m/s, she exerts a force in the opposite direction, causing her to recoil slightly. This change in momentum results in an increase in the astronaut's velocity.
Since momentum is conserved in the absence of external forces, the total momentum before and after the throw must be equal. The momentum before the throw is zero as the astronaut is stationary. Therefore, after the throw, the astronaut and the ball together must have a momentum of [tex]\(200 \times v\)[/tex] kg m/s to compensate for the momentum of the ball, where [tex]\(v\)[/tex] is the velocity of the astronaut after the throw.
The momentum of the ball before the throw is [tex]\(5 \times 0 = 0\)[/tex] kg m/s. Therefore, after the throw, the combined momentum of the astronaut and the ball is [tex]\(5 \times 20 = 100\)[/tex]kg m/s. Since momentum is conserved, the astronaut's velocity after the throw can be calculated as [tex]\(v = \frac{100}{200}\)[/tex] m/s, resulting in [tex]\(v = 0.5\) m/s[/tex]. Finally, the total mass of the astronaut and the ball after the throw can be calculated as[tex]\(200 + 5 = 205\)[/tex] kg, which leads to option C as the correct answer.
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