# Homework Help: Projectile for a game

1. Mar 8, 2005

### bmf59

I'm writing a video game. For the AI i need to be able to calculate the proper initial velocity for a given angle to hit a target a certain x,y distance away. I don't want to use time in the formula. Does any one know a formula for doing this? I found something about a "gunnery law" that looked similar to what i needed, but i couldn't find the formula. Any help would be appreciated since i'm a programmer and not much of a physics person. Thanks.

2. Mar 8, 2005

### Andrew Mason

If the target is at the same height as the launch, you can use:

$$y= vsin\theta t - \frac{1}{2}gt^2$$

where: $$t = \frac{x}{vcos\theta}$$

If x = R (range) and y = 0, you have:

$$vRtan\theta = \frac{gR^2}{v^2cos^2\theta}$$

$$v^3= \frac{gR}{tan\theta cos^2\theta}$$

$$v = \sqrt[3]{\frac{gR}{sin\theta cos\theta}}$$

AM