What Is the Earth's Acceleration Toward a Falling Student?

[map7s]

Homework Statement

A student of mass 72 kg is at an altitude of 1.5 km falling towards the Earth's surface, accelerating at 9.8 m/s2. What is the acceleration of the Earth as it falls toward the student? The radius of the Earth is 6.38 x 10^6 m.

Homework Equations

The Attempt at a Solution

I have no idea how to go about solving this problem. I don't know what to do with the information that is given or even what equations to use. (but I do know that my answer has to have an exponent of 10^-23 m/s2)

 

[Astronuc]

TWO masses exert a force on each other, i.e. F = G M m /r².

The m is subjected to an acceleration of g = G M / r², so can one determine the acceleration of M?

 

[map7s]

oh...okay...that makes more sense...well G is a constant and M is given...so for r, should I use the radius of the earth? (because I was thinking to use the distance that the person was falling b/c that would be the "radius" between the two objects...but then what would I do with the radius of the earth?...and does M correspond to the mass of the Earth or the mass of the person?)

 

[map7s]

is there any other way to do this without using the gravitational force equation?

 

[learningphysics]

is there any other way to do this without using the gravitational force equation?

There is... but I'm guessing they want you to solve it using the gravitational force equation because they give you the radius of the earth.

The Earth experience a net force of GMm/r^2 (here r is not the radius of the earth, but the distance from the center of mass of the Earth to the falling person... ie the radius of the Earth + the altitude), where M is the Earth's mass. So what is the acceleration of the earth?