Question

A 50.0 kg rock starting from rest free falls through a distance of 300.0 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’s velocity. Earth’s mass is 6.0 × 1024 kg. Show all your work, assuming the rock-earth system is closed

Answer 1

Momentum change of the rock = 3835 kgm/s

Chane in earth's velocity = 6.4 x 10⁻²² m/s

Step-by-step explanation:

m = 50.0 kg, M = 6.0 x 10²⁴ kg

d = 300.0 m

final velocity of rock = v, v² = 2gd = 2 * 9.81 * 300, so v = 76.7 m/s

Momentum change of the rock = mv = 50.0 * 76.7 = 3835 kgm/s

Inital momentum of the rock+earth system = 0

final momentum = 0 (momentum conservation)

momentum of rock and momentum of earth are same magnitude and opposite directions.

mv - MV = 0

Chane in earth's velocity = mv/M = 3835/(6.0 x 10²⁴) = 6.4 x 10⁻²² m/s