An astronaut of mass 84.0 kg is taking a space walk to work on the International Space Station. Because of a malfunction with the booster rockets on his spacesuit, he finds himself drifting away from the station with a constant speed of 0.570 m/s. With the booster rockets no longer working, the only way for him to return to the station is to throw the 7.85 kg wrench he is holding.
Which way should he throw the wrench?
away from the station?
toward the station?
He throws the wrench with speed 16.67 m/s WITH RESPECT TO HIMSELF.
After he throws the wrench, how fast is the astronaut drifting toward the space station?
What is the speed of the wrench with respect to the space station?
imfao no sorry
To determine which way the astronaut should throw the wrench, we need to understand the principle of momentum conservation. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. In this case, when the astronaut throws the wrench, an opposing force is exerted on the astronaut due to the principle of conservation of momentum.
The initial momentum of the astronaut and the wrench before the throw is zero since they are both stationary. Therefore, to conserve momentum, the total momentum of the system (astronaut + wrench) after the throw should also be zero.
When the astronaut throws the wrench with a speed of 16.67 m/s relative to himself, the wrench will also have an equal but opposite momentum relative to the astronaut. So, to maintain a total momentum of zero, the astronaut will acquire a momentum in the opposite direction, towards the station.
Therefore, the astronaut should throw the wrench in the direction opposite to the drift, which means the wrench should be thrown towards the space station.
After throwing the wrench, the astronaut's momentum will be equal in magnitude but opposite in direction to the wrench's momentum. Since the wrench's mass is 7.85 kg and its speed is 16.67 m/s, the magnitude of the astronaut's final drift velocity towards the space station will be:
momentum of wrench = momentum of astronaut
(mass of wrench) x (velocity of wrench) = (mass of astronaut) x (final velocity of astronaut)
(7.85 kg) x (16.67 m/s) = (84.0 kg) x (final velocity of astronaut)
Solving for the final velocity of the astronaut, we find:
final velocity of the astronaut = (7.85 kg x 16.67 m/s) / (84.0 kg)
The speed of the wrench with respect to the space station will be the same as the speed of the astronaut after throwing the wrench, as they are now connected by the momentum they acquired in opposite directions.
Therefore, the speed of the wrench with respect to the space station will also be (7.85 kg x 16.67 m/s) / (84.0 kg).