Final answer:
The final velocity of the space capsule moving towards the astronaut is 423.5 m/s.
Step-by-step explanation:
To determine the velocity at which the space capsule is moving towards the astronaut, we can use the law of conservation of momentum. According to this law, the initial momentum of the system (astronaut + space capsule) will be equal to the final momentum of the system.
The initial momentum of the system is given by the sum of the individual momentum of the astronaut and the space capsule. The final momentum is the momentum of the astronaut and the space capsule when they are moving together towards each other.
Let's denote the velocity of the space capsule as Vc and the velocity of the astronaut as Va. The initial momentum is given by:
Momentum = (Mass of astronaut)(Velocity of astronaut) + (Mass of space capsule)(Velocity of space capsule)
After the astronaut pulls on the tether, the momentum of the system becomes:
Momentum = (Mass of astronaut + Mass of space capsule)(Final velocity)
Since the system is initially at rest, the initial momentum is zero.
Therefore, we can set up the following equation:
(Mass of astronaut)(Velocity of astronaut) + (Mass of space capsule)(Velocity of space capsule) = (Mass of astronaut + Mass of space capsule)(Final velocity)
Plugging in the given masses and the velocity of the astronaut, we can solve for the final velocity of the space capsule:
(85 kg)(5.5 m/s) + (1375 kg)(0 m/s) = (85 kg + 1375 kg)(Final velocity)
Final velocity = (85 kg)(5.5 m/s) / (85 kg + 1375 kg)
Final velocity = 423.5 m/s