A 1600 kg object is initially at rest 400 km above the earth’s surface.

[Scarlett]

Homework Statement

A 1600 kg object is initially at rest 400 km above the earth’s surface. The object falls straight
down and generates 8.3x10^8J of heat energy while descending to an altitude of 100 km.
What is the velocity of the object at this altitude?
(http://i1070.photobucket.com/albums/u488/ScatlettArmadillo/Question20.jpg)

Homework Equations

Ek = (mv^2)/2
Ep = -GMm/r
G=6.67^-11
Mass of Earth = 5.98x10^24 kg
Radius of Earth = 6380000 m
Force of Gravity = GMm/r^2

The Attempt at a Solution

http://i1070.photobucket.com/albums/u488/ScatlettArmadillo/Question20-1.jpg
Once I got to the final step I had to find the root of a negative, which is not possible, so I must have made an error somewhere else, but I can't seem to work out where.

 

[Xisune]

Your solution is correct, but the mistake lies in 1/r2 - 1/r1, this equals 6x10^-9, not 7.37 x 10^-12.

 

[Scarlett]

Your solution is correct, but the mistake lies in 1/r2 - 1/r1, this equals 6x10^-9, not 7.37 x 10^-12.

How?
(1/(6380000+100))-(1/(6380000+400))
=(1/6380100)-(1/6380400)
=1.57x10^-7-1.58x10-7
=7.37x10^-12

 

[Scarlett]

Oh, god, I knew I'd've made a stupid mistake, I forgot to convert km to m. Ugh, stupid, but at least I got it now, thanks for the help :)