You jump from a height of 1.0m from the surface of the Earth. The Earth will actually move a bit as you land.
a.) Explain Why
b.) Estimate the distance the Earth moves, listing any assumptions you make
a.) The Earth moves a bit as you land because of Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. When you jump from a height and your feet exert a force on the Earth, the Earth also exerts an equal and opposite force on you. This force causes the Earth to move, although the movement is very small and difficult to perceive.
b.) To estimate the distance the Earth moves, we need to make some assumptions. Let's assume a few things:
1. Your mass is 70 kilograms.
2. The duration of your jump is 0.5 seconds.
3. The average force exerted on the Earth by your jump is 500 Newtons (N).
Using these assumptions, we can calculate the impulse exerted on the Earth using the formula:
Impulse = Force × Time
Impulse = 500 N × 0.5 s = 250 Newton-seconds
Now, we can use the impulse-momentum principle to estimate the change in velocity of the Earth:
Change in velocity = Impulse / Mass of the Earth
First, we need to convert the impulse from Newton-seconds to kilogram-meters per second (kg·m/s):
Impulse (kg·m/s) = 250 N·s × 1 kg / 1 N = 250 kg·m/s
The mass of the Earth is approximately 5.97 × 10^24 kilograms.
Change in velocity = 250 kg·m/s / (5.97 × 10^24 kg)
This calculation yields an extremely small change in velocity for the Earth, which is on the order of 10^-24 m/s. Therefore, the distance the Earth moves when you jump from a height of 1.0m is incredibly minuscule and practically negligible.