Question

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?

Answer 1

Well first of all, you must realize that it depends on how the jumpers are distributed on the earth's surface.  If,say, one billion of them are in the eastern  hemisphere and the other billion are in the western one, then the sum of all of their momenta could easily be zero, and have no effect at all on the planet.  I'm pretty sure what you must have in mind is to consider the Earth to be a block, with a flat upper surface, and all the people jump in the same direction.

average mass per person = 60 kg.
jump velocity = 7 m/s straight up and away from the block, all in the same direction
one person's worth of momentum = (m) (v) = 420 kg.m/s
sum of two billion of them = 8.4 x 10¹¹ kg-m/s all in the same direction

Earth's "recoil" momentum = 8.4 x 10¹¹ in the opposite direction = (m) (v)

Divide each side by 'm' :     v = (momentum) / (mass) =

The Earth's "recoil" velocity is   (8.4 x 10¹¹) / (5.98 x 10²⁴) = 

                                                               1.405 x 10⁻¹³ m/s =

                                               0.00000000014 millimeter per second

I have no intuitive feeling for this kind of thing, so can't judge whether
the answer is reasonable.  But my math and physics felt OK on the
way to the solution, so that's my answer and I'm sticking to it.