- #1
BrettJimison
- 81
- 5
Homework Statement
Good day all! I'm stumped on a question:
If I fire a bullet straight up what will be the initial velocity such that the bullet doesn't come back down?
I need to model a differential equation (it will be first order) some how!
Also, Gravity is not constant, but rather, the acceleration due to gravity dv/dt is -k/r^2 where k is a positive constant and r is the distance to the center of the Earth (4000 mi)
Homework Equations
Also, dv/dt=(dv/dr)v
The Attempt at a Solution
My teacher said something about at the point where the initial velocity is great enough to over come gravity, the root in the de will become complex. That's all I know. Any help would be appreciated!
So far I know:
m(dv/dt)=-mg and g=-k/r^2
I can find a de for v(r) easily since the eqn is seperable, but I'm not sure what to do with it...
Also, the problem gives g at the surface of Earth as -32 ft/s^2, and r in miles, so unfortunately we aren't using metric here.
Thanks!