Projectile for a game

[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.

[Andrew Mason]

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.

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