Initial Velocity in Vector3 format - non equal height

[dklompmaker]

I have been toiling over this for the last three weeks. I am programming a tank to fire at a target. The target can be all over the landscape up, down left right. Currently I have the turret turn to face the target turning the problem into a 2d equation. So I need help finding the right equation for initial velocity to hit the target.

Basically I am doing the following.

tv = target.transform.position - transform.position; // This is a vector direction to my target
var g = -9.8; // Gravity
var r = Mathf.Abs(tv.z); // The range or x to my target
var a = Mathf.Sin(90); /
var v = Mathf.Sqrt((r * g ) / a); // Finally get my velocity and return it
return v;

I know these equations are wrong but I am having a hard time trying to figure out how to account for height differences, and get the correct initial velocity to fire the bullet to hit the target.

Thank you for your help!

 

[LightHero]

The equation you are looking for is the classic two-dimensional trajectory equation. It is derived from Newton's law of motion and allows us to calculate the initial velocity required for a projectile to reach a specified target. The equation is as follows:v₀² = (g * x₀²) / (2 * (y₁ - y₀ + (x₁ - x₀) * tan(θ)))where v₀ is the initial velocity, g is the acceleration due to gravity, x₀ and y₀ are the starting coordinates, x₁ and y₁ are the target coordinates, and θ is the angle of launch. In your case, you are trying to find the initial velocity required to hit a target at some distance away, so the equation simplifies to:v₀² = (g * x²) / (2 * (tan(θ)))Hope this helps!

 

[astrokreng]

I would suggest using the kinematic equations of motion to solve this problem. The initial velocity in vector3 format can be calculated as follows:

1. Determine the displacement vector (tv) from the tank to the target.

2. Decompose the displacement vector into its x, y, and z components.

3. Use the horizontal component of the displacement (tv.x) and the time it takes for the projectile to reach the target (t) to calculate the initial velocity in the x direction using the equation: v0x = tv.x/t.

4. Use the vertical component of the displacement (tv.y) and the time it takes for the projectile to reach its maximum height (t/2) to calculate the initial velocity in the y direction using the equation: v0y = tv.y/(t/2) + 0.5gt.

5. Use the initial velocity in the x and y directions to calculate the magnitude of the initial velocity using the equation: v0 = √(v0x² + v0y²).

6. Use the initial velocity in the z direction (tv.z) and the time it takes for the projectile to reach its maximum height (t/2) to calculate the initial velocity in the z direction using the equation: v0z = tv.z/(t/2) + 0.5gt.

7. Combine the three components of the initial velocity (v0x, v0y, v0z) to get the final initial velocity in vector3 format.

It's important to note that this calculation assumes a constant gravitational acceleration (g) and no air resistance. If these factors are present, the equations may need to be adjusted accordingly.

I hope this helps guide you in finding the correct equation for initial velocity to hit the target. Good luck with your programming!