Two billion people jump up in the air at the same time with an average velocity of 7.0 m/sec. If the mass of

an average person is 60 kilograms and the mass of Earth is 5.98 * 1024 kilograms:

a. What is the total momentum of the two billion people?

b. What is the effect of their action on Earth?

Well, first of all, remember that the Earth is a sphere (ball-shaped).

So chances are that some of the people will jump in exactly the opposite

direction compared to some of the others, and they'll all cancel each other.

But I understand what you're getting at. So let's assume that the Earth

is a big cube, and all the jumpers stand on the same face of the cube and

all jump in the same direction.

Momentum = (mass) x (speed).

The combined momentum of your flash mob is

(2 billion) x (60kg) x (7 m/s) = 8.4 x 10¹¹ kg-m/s.

In order for linear momentum to be conserved, the Earth must move

in the opposite direction with the same momentum.

Earth's momentum = (Earth's mass) x (Earth's speed)

Divide each side by (Earth's mass):

Earth's speed = (Earth's momentum) / (Earth's mass) =

(8.4 x 10¹¹ kg-m/s) / (5.98 * 10²⁴ kg) =

1.4 x 10⁻¹³ m/s.

As the crowd jumps upward, transferring their combined momentum

to the Earth, the Earth moves downward, at the speed of

0.000 000 000 14 millimeter per second.