Two ice skaters stand together as illustrated in the attached figure. They "push off" and travel directly away from each other, the boy with a velocity of v = +0.50 m/s. If the boy weighs 710 N and the girl 480 N, what is the girl's velocity in m/s after they push off? (Consider the ice to be frictionless.)
By definition, the momentum is given by: p = m * v Where, m = mass v = speed. On the other hand, F = m * a Where, m = mass a = acceleration: For the boy we have: p1 = m * v p1 = (F / a) * v p1 = ((710) / (9.81)) * (0.50) p1 = 36.19 Kg * (m / s) For the girl we have: p2 = m * v p2 = (F / a) * v p2 = ((480) / (9.81)) * (v) p2 = 48.93 * v Kg * (m / s) Then, we have: p1 + p2 = 0 36.19 + 48.93 * v = 0 Clearing v: v = - (36.19) / (48.93) v = -0.74 m / s (negative because the velocity is in the opposite direction of the boy's) Answer: the girl's velocity in m / s after they push off is -0.74 m / s
