- #1
Dusty912
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Homework Statement
on a spherical astroid with a radius of 500km and an acceleration due to gravity of 3.0m/s2
How far from the surface will a particle go if it leaves the asteroid’s surface with a radial speed of 1000m/s?
Homework Equations
conservation of energy
Ui + ki=Uf +kf
U=-(GmM)/r
K=(1/2)mv2
-------------------------
f=ma
-(GmM)/r2=ma
-(GM)/r2=a
-(GM)/r=ar
(can apply to h height)
r=radius of astroid
h=height above center
m=mass of rocket
M=mass of astroid
G=gravitational constant
a=acceleration due to asteroids gravity
The Attempt at a Solution
Ui + ki=Uf +kf
Ui + ki=Uf + 0
-(GmM)/r +(1/2)mvi2=-(GmM)/h
the m masses cancel
-(GM)/r +(1/2)vi2=-(GM)/h
-ar +(1/2)vi2=-ah
r-(1/2)(1/a)vi2=h
plugging in the values gives me
500000m+(1/2)(1/(3m/s2)(1000m/s2)2=h
5166666.667meters from the center of the astroid. so 166666.667 meters above its surface. Which is the incorrect answer. the right answer is 250000 meters above the surface.
I know this should be a pretty simple problem, Not too sure where I went wrong. Thanks ahead of time