Can PE with Joe make the world move?

 

The return of PE with Joe has been the best thing this week. He's had the best part of 100000 live streams and when we were all jumping in the air together, I was reminded of the question I have often been asked about whether everyone on planet Earth jumped in the air at the same time and in the same place, would they make the Earth move? I think I can just about manage to jump 50cm into the air doing a tuck jump (he was calling them moon jumps this morning!) From this I can use suvat to calculate my speed when I hit the ground using the equations of uniformly accelerated motion. I'm going to use v^2 = u^2 + 2as. I start falling from the top of my jump when my vertical speed u=0. Acceleration a = 10m/s/s giving the velocity v with which I hit the ground as 3m/s. Now imagine all 7.6 billion of us doing that. Say the average mass is 60kg. Total momentum = 7600000000 x 60 x 3 = 1.4 x 10^12 kgm/s. Suppose we all stop dead and all of that momentum transfers to the Earth. Mass of Earth = 6 x 10^24kg. That gives the Earth a speed of 0.00000000000002m/s In other words, the Earth won't move.