Question

At time t = 0 two figure skaters are moving together over ice with negligible friction, as shown above. Skater 1, represented by the large black dot, is twice as massive as skater 2, represented by the gray dot. At t = 2 s the skaters push off of one another. The location of skater 1 is shown at t = 4 s . At t = 4 s , skater 2 is located at which of the labeled points?

Answer 1

The exact location of skater 2 at t = 4 s cannot be determined without more specific information.

Step-by-step explanation:

In order to answer the question, we need more specific information about the labeled points and the directions in which the skaters are moving. However, we can provide some general information about the motion of the skaters.

If skater 1 is pushing off of skater 2, then according to Newton's third law of motion, skater 2 will experience an equal and opposite force exerted by skater 1. This force will cause skater 2 to accelerate in the direction opposite to the force. Therefore, at t = 4 s, skater 2 would most likely be located in a position that is opposite to the direction in which skater 1 is moving.

Without more specific information about the labeled points and the directions of motion, it is not possible to determine the exact location of skater 2 at t = 4 s.

Answer 2

Skater 2 will be located at the point in the opposite direction to Skater 1 and twice the distance away at t = 4s.

To find Skater 2's location at t = 4 s, apply conservation of momentum principles, considering the skaters' relative masses and velocities after they push off from one another.

The question is about the conservation of momentum when two figure skaters push off each other on ice with negligible friction. If Skater 1, who is twice as massive as Skater 2, is at a certain point at t = 4 s, then Skater 2 must be at a point that reflects the conservation of momentum.

Momentum is conserved because the force each skater exerts on the other is equal in magnitude and opposite in direction (Newton's third law), and with negligible friction, there is no external force acting on the system. The momentum of the system before they push off is zero (as they are moving together), and after they push off, the total momentum must still be zero.

This means if Skater 1 is at a certain point at t = 4 s, Skater 2 must be at a point twice as far from the original location as Skater 1 (since they have half the mass and, therefore, must have twice the velocity to have the same amount of momentum).