Question

Two hockey players push off from a clinch, recoiling from rest. Jean-Claude has an inertia that is 60% greater than Pierre's inertia. After they push off and move across the ice in opposite directions, they lose kinetic energy at the same rate until they come to a stop.

1.What is the ratio of the distances which players traveled?

Answer 1

$$m_2=1.6m_1$$

From the conservation of momentum:

$$m_1v_1=m_2v_2\to v_1=1.6v_2$$

$$K_{10}=0.5m_1v_1^2$$

$$K_{20}=0.5m_2v_2^2=\frac{K_{10}}{1.6}=0.625K_{10}$$

$$\frac{d_{JC}}{d_P}=\frac{K_{20}}{K_{10}}=0.625$$