Answer:
(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.
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.
Answer:
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