Question

Suppose the entire population of the world gathers in ONE spot and everyone jumps at the sound of a prearranged signal. While everyone is in the air, does the Earth gain momentum in the opposite direction?a) No, the inertial mass of Earth is so large that the planet's change in motion is imperceptibleb) Yes, however the change in momentum of Earth is much less than that of all the jumping people because of Earth's large inertial massc) Yes, Earth recoils like that of a rifle firing a bullet with a change in momentum equal to and opposite of peopled) It depends

Answer 1

(b) Yes, the earth gains momentum but the change in momentum of the earth is much lesser compared to that of everyone in the air. The resistance to motion (inertia of the earth), which is a function of its mass is so great that the earth's acceleration is small in the given time frame.

Step-by-step explanation:

From Newton's second law which can be stated mathematically as

F = m(v-u)/t = ma.

By Newton's law of gravitation, there is a force between the earth and everyone in the air. This force is responsible for the change in momentum of everyone in the air and this force gives them an acceleration equal to g = 9.80m/s². By Newton's law of gravitation and Newton's third law of motion, this force is also equal to the force exerted by everyone on the earth.

For this to be true,

F = M (everyone) ×a (everyone) = M(earth) × a (earth).

And

a (earth) = {M (everyone) ×a (everyone) }/M (earth)

Then

a (earth) must be lesser than a (everyone) since M(earth) >> M(everyone).

a = change in momentum/ time

Therefore the earth will have a much lesser change in momentum which is the reason we won't notice the earth's movement.

Thank you for reading.