Question

Two ice skaters, with masses of 30.0 kgkg and 75.0 kgkg , are at the center of a 60.0 mm -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 40.0 ss , how long does the lighter skater take to reach the edge?

Answer 1

Let

m1 = 75 kg

m2 = 30 kg

The final momentum must be zero as they come to rest

so,

m1v1f + m2v2f = 0

m1v1f = - m2v2f

v1f / v2f = - m2 / m1

v1f / v2f = - 30 / 75

v1f / v2f = - 0.4 ---- (1)

let x be the distance traveled by each skaet.

If heavier skater travles 'x' then lighter skater travels '-x'

so,

x = 40 * v1f

and

-x = t2 * v2f

the distance is same

x = -x

40 * v1f = - t2 * v2f

v1f = - t2 * v2f / 40 ------ (2)

using (1) and (2)

- 0.4 * v2f = - t2 * v2f / 40

0.4 = t2 / 40

t2 = 16 seconds