Question

Two ice skaters, with masses of 50.0kg and 65.0kg , are at the center of a 40.0m -diameter circular rink. The skaters push off against each other and glide to opposite edges of the rink.

If the heavier skater reaches the edge in 30.0s , how long does the lighter skater take to reach the edge?

Express your answer with the appropriate units.

Answer 1

For heavier skater ,

d =ut

u = 20 / 30 = 2/3 m/s

now for pushing using , momentum conservation

initial = final

0 = 50v + 65 x (2/3)

v = 0.867 m/s

t = d/v = 20 / 0.867   = 23.08 sec

Answer 2

Using momentum= mass x velocity and velocity = displacement / time

You know that the heavier one takes 30 seconds to reach the side and that he moves 20 metres to the side so you can use conservation of momentum. ( I'm taking the heavier one's velocity to be positive )

0 = (65 x 20/30) + (30 x -20/t) -------> 0 = 43.33 - 600/t -------> 600/t = 43.33 ------> 600/43.33 = t

therefore t = 13.8568 seconds