Physics-High School

Question

A 14kg rock starting from rest free falls through a distance of 5.0 m with no air resistance. Find the momentum change of the rock caused by its fall and the resulting change in the magnitude of earth velocity. Earth's mass is 6.0*10^24 kg.

Answer 1

Using Vfinal^2 = Vinitial^2 + 2a(delta y), the velocity of the rock when it hits the earth is 9.9 m/s. The momentum of the rock is then m x v = 140 Kgm/s (which is it's change in momentum since it essentially stops). Momentum is conserved, so the new mass of the combined earth/rock system (14 + 6.0*10^24) x velocity of this system = 140 Kgm/s. So the velocity change = 140/(14+6*10^24) = 2.3*10^-23 m/s