2 Billion People Jumping Off Ladders Simultaneously

[Idioticsmartie]

Homework Statement

Let us say there are 2 billion people with an average mass of 50 kg. They all climb ladders which are 1 meter tall. At a particular instant they all jump off nd land on the ground simultaneously. This is an inelastic collision with the Earth. Assume the Earth does not move prior to the collision

Homework Equations

0.5m[tex]_{a}[/tex]v[tex]^{2}_{a}[/tex] + 0.5m[tex]_{b}[/tex]v[tex]^{2}_{b}[/tex] = 0.5m[tex]_{a}[/tex]v[tex]^{'2}_{a}[/tex] + 0.5m[tex]_{b}[/tex]v[tex]^{'2}_{b}[/tex]

v[tex]^{2}[/tex] = v[tex]^{2}_{0}[/tex] + 2a(x-x[tex]_{0}[/tex])

The Attempt at a Solution

I think I can solve this, I'm just confused about whether or not the initial velocity for the people is 0 (before they all jump) or if it's 4.29 m/s (their speed just before they collide with the earth)

Or would it work either way?

 

[learningphysics]

Are you supposed to find the velocity of the Earth after the collision?

It's an inelastic collision... so you can't use conservation of kinetic energy.
You need to use conservation of momentum...

Find the velocity with which the people hit the ground... then use conservation of momentum.

 

[Idioticsmartie]

so the initial velocity of the people is 0, before they jump, right?

 

[Doc Al]

so the initial velocity of the people is 0, before they jump, right?

Sure.

What are you supposed to figure out? Are the people evenly spaced around the earth?

 

[Idioticsmartie]

No, they're all in China. So I just need to find the velocity of the Earth afterwards. And figure out realistically if the center of mass changes during the collision, which it doesn't, because the Earth accelerates towards the people, doesn't it?

 

[Doc Al]

That's right. Since there are no external forces, the center of mass of Earth + people doesn't change no matter what they do.

Do as learningphysics suggested.

 

[Idioticsmartie]

Great - thanks!

 

[Idioticsmartie]

Wait, sorry - is the velocity prime (aka after the collision) the same for both people and earth, since they become one object?

 

[learningphysics]

Wait, sorry - is the velocity prime (aka after the collision) the same for both people and earth, since they become one object?

Yes... if it is given that the people don't bounce back up from the earth.