Newton's Laws?

Question

You stand on a chair and jump off
The Earth is lurching up toward you with acceleration a.
If your mass is 96 kg, what is value of a?
If the seat of chair is 30 cm off ground, how far does Earth move while you are falling?

Answer 1

Using Newton's Law of Universal gravitation,
F = (GMm)/r^2
Using Newton's Second Law of Motion,
Ma = (GMm)/r^2
a = (6.67x10^(-11)x(96))/(r^2)
If given radius, you can find a. Using value from wikipedia, r = 6,371.01 km = 6.37101 x 10^(6) m
Thus, a = 1.58 x 10^(-22) m/s^2

If given mass of earth,
Normally, g = 9.81N/kg while you are near the Earth.
Hence, g = (GM)/r^2 = 9.81N/kg
Substituting, F = (9.81)(96) = 941.76N
(M)(a) = 941.76N
Using value from wikipedia, M = 5.9736×10^(24) kg
Thus, a = 1.58x10^(-22) m/s^2

Time taken for you to reach the ground = t
Given s = 30cm = 0.30m, a=g=9.81m/s^2, u = 0m/s
s = ut + 0.5at^2
0.30 = 0 + 0.5(9.81)t^2
solving, t = 0.247s

For earth, Assume that you are the only one jumping,
t = 0.247s, a = 1.58x10^(-22) m/s^2, u = 0m/s, find s
using s = ut + 0.5at^2
s = 0 + 0.5 (1.58x10^(-22))(0.247)^2
Thus, s = 4.83x10^(-24) m

Answer 2

The earth is exerting a force of 96 x10 = 960 N on You.

By reaction you are exerting the same amount of force on the earth.

Hence the acceleration of earth is 960/ M where M is the mass of earth.
a = 960 / 6x 10^24 = 1.6e-22 m/s^2.
The acceleration acting on you is 10m/s^2.

The distance moved by earth is practically nil.

Answer 3

Need to know the mass of the Earth. Then calculate the mass ratio of the Earth to you, and divide the 30 cm in that ratio. You're right. The center of mass of the system does move.

Doug

Answer 4

a=9.8 m/s^2
the earth moves the same amount as u do. 30 cm wich is very small compared to the size of earth, but this is on his sec law, each and every action has equal and opposite reaction.