Two skaters, one with mass 62 kg and the other with mass 45 kg, stand on an ice rink holding a pole of length 10 m and negligible mass. Starting from the ends of the pole, the skaters pull themselves along the pole until they meet. How far does the 45 kg skater move?

To solve this problem, we need to apply the principle of conservation of momentum. The total momentum before the skaters move is equal to the total momentum after they move.

Before the skaters start moving, both skaters and the pole are at rest, so the total momentum is zero. After they move, the skaters meet at the center of the pole, and their momentum after the move will also be zero because they are again at rest.

The momentum is given by the product of an object's mass and velocity. Let's assume the 62 kg skater moves toward the 45 kg skater.

Let's denote the distance moved by the 45 kg skater as x. The 62 kg skater will move (10 - x) meters since the pole is 10 meters long.

Since momentum is conserved, we have:

(45 kg) * v1 + (62 kg) * v2 = 0

Here, v1 and v2 are the respective velocities of the skaters after moving. Since both are at rest, their velocities are zero.

So we can solve the equation:

(45 kg) * 0 + (62 kg) * 0 = (45 kg) * v1 + (62 kg) * v2

0 = (45 kg) * 0 + (62 kg) * 0

0 = 0

As we can see, the equation satisfies the condition. The velocity of the skaters after moving is zero, which means they are at rest.

Now, let's find the distances moved by each skater:

Distance moved by the 45 kg skater = x
Distance moved by the 62 kg skater = 10 - x

Since the total distance is 10 meters (the length of the pole), we can write:

x + (10 - x) = 10

Combining like terms, we get:

10 = 10

This equation is true for any value of x, which means that the 45 kg skater can move any distance along the pole. The distance moved by the 45 kg skater can range from 0 to 10 meters.

They meet at the center of mass, which does not move.

Measured from the original 45 kg skater location, the CM is 620/107 = 5.79 m away.

That is how far that skater moves.