What Is the Initial Velocity Formula for Projectile Motion in Game Development?

[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 anyone 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 anyone 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

 

[thepatientmental]

As a physics enthusiast, I would be happy to assist you with your question. The formula you are looking for is known as the projectile motion equation, which takes into account the initial velocity, angle of launch, and distance to the target. It is often written as x = v0*cos(theta)*t and y = v0*sin(theta)*t - 0.5*g*t^2, where x and y represent the horizontal and vertical distance traveled by the projectile, v0 is the initial velocity, theta is the angle of launch, t is the time, and g is the acceleration due to gravity.

To solve for the initial velocity, you can rearrange the equations to v0 = x/(cos(theta)*t) and v0 = (y + 0.5*g*t^2)/sin(theta)*t. You can then plug in the desired x and y distances and the angle of launch to calculate the initial velocity needed to hit the target. This method does not involve time in the formula, as requested.

I would also recommend looking into the concept of trajectory and how it relates to projectile motion, as it can help you better understand and implement the formula in your game. Best of luck with your project!