Principle of Conservation of Linear Momentum?

Lissette Semon: The skaters are initially stationary, so their combined momentum is 0.Let u1 and u2 be their respective velocities just as they separate, with u1 in the positive and u2 in the negative direction.Then their combined momentum is m1u1 - m2u2.By the Principle of Conservation of Linear Momentum, 0 = m1u1 - m2u2.∴ m1u1 = m2u2.∴ m1/m2 = u2/u1. (Eqn. 1)Now consider the equation for uniformly accelerated motion:v² = u² + 2as,where v is final velocity, u is initial velocity, a is acceleration, s = displacement.For both skaters, v = 0 and a is the same.Skater 1 glides twice as far, so let skater 2 glide x and skater 1 glide 2x.Thus we can write down two equations:For skater 1, 0 = u1² + 2a*2x => u1² = -4ax.For skater 2, 0 = u2² + 2ax => u2² = -2ax.∴ u2²/u1² = 1/2.∴ u2/u1 = 1/√2.Hence, from (1), m1/m2 = 1/√2....Show more