posted by Rene on .
Two ice skaters, with masses of 30kg & 85 kg are at the center of a 30m diameter circular rink. The skaters push off against each other & glide to opposite edges of the rink. If the heavier skater reaches the edge in 40s, how long does the lighter skater take to reach the edge?
Let the lighter skater have mass M1 and velocity V1 after pushing off. For the heaver skater, use M2 and V2.
Because of conservation of momentum,
M1 V1 + M2 V2 = 0
V1/V2 = -M2/M1 = -2.833
(The minus sign just means they go in opposite drections)
They both travel equal distances to the end of the rink. The time to get there is inversely proportional to the velocity and proporitonal the mass.
T2/T1 = |V1/V2| = M2/M1 = 2.833
You know that T2 = 40 s
Solve for T1