Newtons laws question?

Question

A student with mass 47.0 kg jumps off a high diving board.
Using 6.00×1024 kg for the mass of the earth, what is the acceleration of the earth toward her as she accelerates toward the earth with an acceleration of 9.80 m/s^2? Assume that the net force on the earth is the force of gravity she exerts on it.

Best answer gets 10pts.

Answer 1

F = -G(m1*m2)/r^2
F = force
G = gravitational constant = (6.6742 +/- 0.001)*10^(-11) N * m^2 / kg^2
m1 = mass of object 1 = 47 kg
m2 = mass of object 2 = 6.00×10^24 kg
r = distance between objects

F = -(6.6742 +/- 0.001)*10^(-11) * (47 kg * 6.00*10^24 kg) / r^2
F = -4.225 * 10^14 N*m^2 / r^2
Since the distanct between the Earth and the person weren't given this is all the farther the force can be calculated to. The force will be equal on both the objects (person and Earth) only that the acceleration of the Earth will be almost nothing due to its size and the force will be in the opposite direction.

But based on the acceleration of the person, you can calculate a force, but it will only be an estimate
F = m*a = 47 kg * 9.8*10 m / s^2 = 460.6 N
Force on Earth is 460.6 N

Now the acceleration of the Earth is
460.6 = 6.00*10^24 * a
a = 7.68 * 10^(-23) m/s^2

Answer 2

According to Newton's third law, every action has an equal and opposite reaction.
The same force the girl pulls on the earth with her gravity is equal to the force the earth pulls on her with its gravity.

F(girl) = F(earth)
ma(girl) = ma (earth)
47*9.8 = 6x10^24 * a
a = 7.67x10^-23 m/s/s

simple, just need to keep in mind all of Newton's three laws :)

Answer 3

F=Ma=mg
a=mg/M
a=76,76*10^-24 m/s^2

Answer 4

the force of earth on her is the same as her on the earth. you have masses and acceleration, you can claculate it.

Answer 5

after my 9th grade science class, i NEVER want to hear the words "newtons laws" again

Answer 6

Do your homework yourself.