# Geometry to work out how fast a bullet would have to travel to

1. Sep 8, 2012

### Hazzattack

Hi guys, i was wondering how you calculate how fast a bullet would have to travel to 'overcome' gravity, i.e if it didn't hit anything (and discluding air resistance for now).
Mapping the earth as a circle and knowing things such as the radius of the earth and gravity acts on the bullet at 9.81 m/s^2 - how would i draw the triangles inside the circle to calculate the speed the bullet needs to travel to continue moving around the earth (i.e the surface drops off at the same rate as the acceleration of gravity).

I wanted to solve the problem using geometry - which i'm aware would be a crude approximation. I couldn't find anything helpful via searching the internet, just continuous about which hits the ground first.... blablabla.

Thanks a lot for any help,

2. Sep 8, 2012

### Redbelly98

Staff Emeritus
Are you familiar with the equation for centripetal force, i.e. the force required to keep an object moving in a circular path at constant speed? That force is $\frac{mv^2}{r}$, where m is the object's mass, v is it's speed, and r is the radius of the circular path.

Set that force equal to the gravitational force acting on the object -- since it is gravity that provides the necessary force -- and then you can figure out what v is.

p.s. I am not sure how drawing triangles would help out here.

Last edited: Sep 8, 2012
3. Sep 8, 2012

### K^2

There is a way of deriving mv²/r geometrically, which does involve triangles. It involves taking a limit as the final step, but it's a pretty simple proof. Could that be part of what OP is referring to?

4. Sep 8, 2012

### Hazzattack

I am familiar with it, and admittedly, your way of solving the problem is far simpler. I found it in feynmanns lectures, chapter 7 I think, just after he talks about keplers laws. He solves this problem via geometry, but I found the calculation a little confusing (not due to its complexity). I'll take a picture of it later and upload it. Thanks for the responses.