Suppose that three astronauts outside a spaceship
decide to play catch. All the astronauts weigh the same on
Earth and are equally strong. The first astronaut throws
the second astronaut toward the third one and the game
begins. Describe the motion of the astronauts as the game
proceeds. How long will the game last?
idk what it is
To describe the motion of the astronauts during the game, we need to consider the principle of conservation of momentum. According to this principle, the total momentum of a system remains constant if no external forces act upon it. In this case, since there are no external forces acting on the system (ignoring the negligible effects of gravity), the total momentum of the three astronauts will be conserved.
Initially, when the first astronaut throws the second astronaut towards the third one, the first astronaut imparts an initial momentum to the second astronaut. As a result, the second astronaut begins to move towards the third astronaut.
Since the second astronaut has mass and is moving, they also possess momentum. When the second astronaut reaches the third astronaut, they transfer part of their momentum to the third astronaut through the act of catching. As a result, the third astronaut starts to move in the opposite direction of the second astronaut.
Meanwhile, the second astronaut experiences a change in momentum due to the transfer to the third astronaut. This change results in the second astronaut moving in the opposite direction of their initial motion.
Now, the third astronaut possesses the combined momentum of the second astronaut and themselves. They can then throw the second astronaut back towards the first astronaut, transferring part of their momentum to the second astronaut.
The same process repeats as before, but now with the second astronaut moving in the opposite direction. The game can continue back and forth until the astronauts decide to stop or until some external force disrupts their motion.
As for how long the game will last, it depends on the specific velocities and distances involved, as well as the strength and accuracy of the astronauts' throws and catches. The time it takes for each astronaut to move towards and away from each other can be calculated by dividing the distance between them by the speed at which they are moving.