An unlikely weapon was once proposed which had all of the people in China to jum

Question

An unlikely weapon was once proposed which had all of the people in China to jump up and down simultaneously. Let us say there are 2 billion people (2.0 x 10^9) with an average mass of 50 kg. They all climb ladders which are 1 meter tall. At a particular instant they all jump off nad land on the ground simultaneously. This is an inelastic collision with the Earth. Assume the Earth does not move proior to the collision.

Calculate what the speed of the Earth and the people would be after the collision.

(Hint: Treat the people as one object.

Caveat: In actuality the Earth would accelearte slightly towards the people as they fell, we will ignore any initial speed the Earth may have at the time of collision.)

Explanation / Answer

Mass of Earth = 5.972*10^24 kg

so 2.0*10^9*50 *v = (2.0*10^9*50 + 5.972*10^24 )v'

v = sqrt(2*9.8*1) =4.427 m/s

v' = 7.41*10^-11 m/s

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