Question

Two ice skaters, with masses of 77 kg and 55 kg , stand facing each other on a 19-m -wide frozen river. the skaters push off against each other, glide backward straight toward the river's edges, and reach the edges at exactly the same time. how far did the 77 kg skater glide?

Answer 1

The 77 kg skater glides approximately 14.27 m.

Step-by-step explanation:

When the two ice skaters push off against each other, they experience equal and opposite forces according to Newton's third law of motion. Therefore, the momentum of the system of skaters is conserved. The momentum before the push-off is zero because the skaters are at rest, so the total momentum after the push-off is also zero. Since the two skaters reach the edges of the river at the same time, their displacements and velocities must be equal.

Let's assume the distance the 77 kg skater glides is d. Since the total displacement is 19 m, the 55 kg skater also glides a distance of 19-d. Since their velocities are equal, we can set up an equation:

77 kg skater's velocity = 55 kg skater's velocity

 

By substituting the values, we can solve for d:

 

After solving, we get d = 14.27 m. Therefore, the 77 kg skater glides approximately 14.27 m.