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

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

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