Two ice skaters stand facing each other at rest on a frozen pond. They push off against one another and the 48 kg skater acquires a speed of 0.68 m/s. If the other skater acquires a speed of 0.89 m/s, what is her mass in kilograms?
To solve this problem, we can use the principle of conservation of momentum.
According to the principle of conservation of momentum, the total momentum before the push is equal to the total momentum after the push.
Let the mass of the second skater be M kg and her initial velocity be u m/s. The momentum before the push is 0, as both skaters are at rest.
After the push, the momentum of the first skater is given by:
M1 = 48 kg
V1 = 0.68 m/s
The momentum of the second skater is given by:
M2 = M kg
V2 = 0.89 m/s
Therefore, according to the conservation of momentum:
M1u1 + M2u2 = M1V1 + M2V2
Substitute the known values:
48*0 + M*u = 48*0.68 + M*0.89
0 = 32.64 + 0.89M
0.89M = -32.64
M = -32.64 / 0.89
M = 36.71 kg
Therefore, the mass of the second skater is approximately 36.71 kg.