Two ice skaters have masses m1 and m2 and are initially stationary. Their skates

Question

Two ice skaters have masses m1 and m2 and are initially stationary. Their skates are identical. They push against one another, as in Figure 7.10, and move in opposite directions with different speeds. While they are pushing against each other, any kinetic frictional forces acting on their skates can be ignored. However, once the skaters separate, kinetic frictional forces eventually bring them to a halt. As they glide to a halt, the magnitudes of their accelerations are equal, and skater 1 glides twice as far as skater 2. What is the ratio m1/m2 of their masses?

Explanation / Answer

v^2 - u^2 = 2as Here v = 0 for both skaters.... Hence u^2 = 2 as Let u1 and u2 be the initial velocities of the two skaters... u1^2 / u2^2 = 2as1 / 2as2 = s1 / s2 = 2 u1 / u2 = 1.414 m1u1 = m2u2 so, m1 / m2 = u2 / u1 = 1 / 1.414 = 0.707

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