Question

Two ice skaters, with masses of 67 kg and 53 kg , stand facing each other on a 13-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.

Answer 1

V1 = speed of 67 kg ice skater
V2 = speed of 53 kg ice skater
momentum of 67 kg ice skater = 67(V1)
momentum of 53 kg ice skater = 53(V2)
Conservation of Momentum:
67(V1) = 53(V2)

x1 = distance of 67 kg ice skater from edge of river
x2 = distance of 53kg ice skater from edge of river
x1 + x2 = 13 m
x2 = 13 - x1 <=
t = time each skater takes to reach edge of river

V1 = x1/t
V2 = x2/t
67(x1/t) = 53(x2/t)
multiply both sides by t
67(x1) = 53(x2)
67(x1) = 53(13-x1) = 689 - 53(x1)
120(x1) = 689
x1 = 689/120 ≈ 5.74 m ................................ANS