Object being launched into space

[aeromat]

Homework Statement

Complete the chart for a 1kg rock and its trip through the Earth's gravitational firled. The rock was powerfully launched straight up from the surface of the Earth at 1x10^4 m/s.

Note: An object's kinetic energy must be a (+)-value; a negative value is impossible.

Homework Equations

Eg = -GmM/r
Ek = GMm/2r
mEarth = 6*10^24 kg
Re = 6.4*10^6 m

The Attempt at a Solution

Basically, we had to set distance as a variable, and see how the energies (Ek and Eg) would change.
The total energy is constant, and it is found to be -1.25*10^7 J
Ok If I solve for E for instance, 6 times the radius of the earth, I will get -1.04x10^7 J of Eg. However, when I try to solve for Ek:

Ek + Eg = ET
Ek = ET - Eg
Ek = (-) answer, since the Eg was smaller than the overall ET, which was found to be -1.25*10^7.

Is this still valid?

 

[xiaoB]

mEarth = 6*10^4 kg

The mass of the Earth should be ~ 6x10²⁴ kg:shy:

 

[gneill]

If the total mechanical energy of the rock is -1.25*10⁷ J, a negative value, then the rock is bound by the Earth's gravity and will not escape. That means that there is a maximum distance it can achieve before it returns to Earth. You should find this distance to make sure that you don't go plugging in distances that it cannot achieve: you'll get nonsense results like negative KE's.