Final answer:
To calculate the time it takes for the astronaut to return to the spaceship, we can use the principle of conservation of momentum.
The initial momentum of the astronaut and the spaceship is given by the mass of the astronaut multiplied by the velocity of the astronaut, and the final momentum is given by the mass of the astronaut plus the mass of the tool bag, multiplied by their common velocity after the throw.
By solving for the common velocity and then using the equation distance = velocity x time, we can calculate the time it will take for the astronaut to return to the spaceship.
Step-by-step explanation:
To calculate the time it takes for the astronaut to return to the spaceship, we can use the principle of conservation of momentum.
The initial momentum of the astronaut and the spaceship is given by the mass of the astronaut multiplied by the velocity of the astronaut, and the final momentum is given by the mass of the astronaut plus the mass of the tool bag, multiplied by their common velocity after the throw.
Since momentum is conserved, we can set the initial momentum equal to the final momentum and solve for the common velocity.
Initial momentum = Final momentum
(100 kg)(0.1 m/s) = (100 kg + 10 kg)(common velocity)
Solving for the common velocity, we find that it is equal to 0.09 m/s. Now, we can calculate the time it will take for the astronaut to return to the spaceship by using the equation distance = velocity x time.
Distance = 10 m (since the astronaut is 10 m away from the spaceship)
Velocity = 0.09 m/s
Time = Distance / Velocity = 10 m / 0.09 m/s = 111.11 seconds.
Since the question asks for the answer in seconds, we round the result to the nearest whole number, which is 111 seconds. None of the given answer choices match this result, so we cannot determine the exact time it will take for the astronaut to return to the spaceship based on the information provided.