# Homework Help: Using Gravitational constant to get the final velocity

1. Nov 24, 2008

### hyperkkt

1. The problem statement, all variables and given/known data
Evil Alien has put an Asteroid with
mass of 1,000,000kg to destroy mankind.
Distance from center of the Earth to Asteroid
(assume negligible center) is
10^8m and lets the gravitational force do the work.
Earth radius is 6.4 x 10^6m
and its mass is 5.98 x 10^24kg.
If the atmosphere extends out to 500km beyond
the surface and exrts an average friction force of 10^8N,
calculate the speed of the asteroid just before it hits the ground.
(Assume the asteroid rtains all of its mass as it travels through the atmosphere)

2. Relevant equation
Fgrav = Gm1m2/r^2

3. The attempt at a solution

I tried to use F=ma first
by doing it so I get
F=Gm1m2/r^2=m1a
a=Gm2/r^2

However, could not do anything more since there is no dt.

So, I tried taking an integral of it,
finding the work and set it equal to kinetic energy
(not sure whether indefinite/definite integral matters)
integral of Gm1m2/r^2 = -Gm1m2/r
-Gm2/r^2=v^2
but got this and it cannot happen
because v^2 cannot be - number...
v=i(imginary)

I am stuck at this point have no
further suggestion on what I should do.

I've been working on it for about an hour
and would appreciate any help.

Last edited: Nov 24, 2008
2. Nov 24, 2008

### Dick

The potential energy PE(r)=-G*m1*m2/r. You find the change in potential energy by subtracting PE(r=10^8m)-PE(r=radius of the earth). The difference is positive, not negative.

3. Nov 24, 2008

### hyperkkt

Oh I see, but how do you get v after finding the change in PE?
And from there how do I apply it to the interval which frictino decreases the speed?

I may be understanding something wrong.