Answer :
Jennifer begins to move towards her spaceship at a speed of approximately 0.462 m/s.
We are dealing with the conservation of momentum. The principle states that the total momentum of a closed system is constant if no external forces act on it. When Astronaut Jennifer throws the wrench, the system (consisting of Jennifer and the wrench) must conserve its total momentum.
Given Data:
Mass of the wrench (m): 6 kg
Velocity of the wrench (v): 15 m/s (away from the spaceship)
Combined mass of Jennifer and her spacesuit (M): 195 kg
Initially, Jennifer and the wrench are stationary relative to the spaceship. Therefore, their initial momentum is 0.
After Jennifer throws the wrench, the wrench moves away from the spaceship, and Jennifer starts moving toward the spaceship. According to the conservation of momentum:
[tex](Initial Momentum) = (Final Momentum)[/tex]
i.e.,
[tex]0 = M \cdot V + m \cdot v[/tex]
where:
V is Jennifer's velocity towards the spaceship (which we need to find).
v is the velocity of the wrench (15 m/s).
Because momentum is a vector quantity and direction matters,
[tex]M \cdot V = - m \cdot v[/tex]
So,
[tex]V = \frac{- m \cdot v}{M}[/tex]
Plug in the given values:
[tex]V = \frac{- 6 \ kg \cdot 15 \ m/s}{195 \ kg}[/tex]
Calculate:
[tex]V = \frac{- 90 \ kg \cdot m/s}{195 \ kg}[/tex]
[tex]V \approx -0.462 \ m/s[/tex]
The negative sign indicates that Jennifer's velocity is towards the spaceship (opposite to the direction in which she threw the wrench).
