You stand on a skateboard at rest and throw a rock at 5 m/sec. You move back at 0.5 m/ sec. What is the combined mass of you and the skateboard?
10 times the mass of the rock
From conservation of momentum,
Your change in momentum + the Rock's change in momentum = 0
(Your mass)(Your change in velocity) + (Rock's mass)(Rock's change in velocity) = 0
(Your mass)(-0.5m/s) + (Rock's mass)(5m/s) = 0
Your mass = 10 (Rock's mass)