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Posted: **Mon Apr 21, 2014 2:39 am**

I think this wikipedia article would be a good read.

Posted: **Mon Apr 21, 2014 3:59 pm**

Wikipedia could help if I had any understanding of math : )))
It's all potat for me https://dl.dropboxusercontent.com/u/876 ... ipedia.gif

From stackoverflow:

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T_x = s_x * t
T_y = -0.5 * g * (t ^ 2) + s_y * t

So
T_x is the distance
s_x is my x velocity
t is calculated with t = T_x / s_x

With t I could calculate s_y (???)

Posted: **Mon Apr 21, 2014 9:08 pm**

Shouldn't you already have your s_y? It would just be your player's y-velocity, like the x-velocity.
Now, if you want t_y, it would be like calculating your t_x.

I'll try to get the Wikipedia formulas for you:

Conditions at the final position of the projectile
Distance traveled
- The total horizontal distance (d) traveled.

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Distance = ( ( Velocity * math.cos( LaunchDegrees ) ) / Gravity ) * ( Velocity * math.sin( LaunchDegrees ) + math.sqrt( ( Velocity * LaunchDegrees ) ^ 2 + ( 2 * Gravity * InitialLaunchY ) ) )

Note that I'm not sure if it needs it in degrees or radians, I'm just assuming degrees. If that's the case, you may need to use math.deg. If not, you'll need to use math.rad (depending on how you store the angle, that is). THIS GOES FOR ALL OF THESE
- When the surface the object is launched from and is flying over is flat (the initial height is zero), the distance traveled is:

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Distance = ( Velocity ^ 2 * math.sin( 2 * LaunchAngle ) ) / Gravity

Time of Flight
- The time of flight (t) is the time it takes for the projectile to finish its trajectory.

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Time = Distance / ( Velocity * math.cos( LaunchAngle ) )

or

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Time = ( Velocity * math.sin( LaunchAngle ) + math.sqrt( ( Velocity * math.sin( LaunchAngle ) ^ 2 + ( 2 * Gravity * InitialLaunchY ) ) ) ) / Gravity

Angle of reach
- The "angle of reach" (not quite a scientific term) is the angle (φ) at which a projectile must be launched in order to go a distance d, given the initial velocity v.

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Angle = .5 * math.asin( ( Gravity * Distance ) / ( Velocity ^ 2 ) )

Conditions at an arbitrary distance x
Height at x
- The height y of the projectile at distance x is given by

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y = InitialLaunchY + x * math.tan( LaunchAngle ) - ( ( Gravity * x ^ 2 ) / ( 2 * ( Velocity * math.cos( LaunchAngle ) ) ^ 2 ) )

The third term is the deviation from traveling in a straight line.
Velocity at x
- The magnitude, |v|, of the velocity of the projectile at distance x is given by

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Velocity = math.abs( math.sqrt( InitialVelocity ^ 2 - ( 2 * Gravity * x * math.tan( LaunchAngle ) + ( ( Gravity * x ) / ( InitialVelocity ) * math.cos( LaunchAngle ) ) ^ 2 ) ) )

Angle \theta required to hit coordinate (x,y)

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Angle1 = math.atan( ( InitialVelocity ^ 2 + math.sqrt( InitialVelocity ^ 4 - Gravity * ( Gravity * TargetX ^ 2 + 2 * TargetY * InitialVelocity ^ 2 ) ) ) / ( Gravity * TargetX ) )
Angle2 = math.atan( ( InitialVelocity ^ 2 - math.sqrt( InitialVelocity ^ 4 - Gravity * ( Gravity * TargetX ^ 2 + 2 * TargetY * InitialVelocity ^ 2 ) ) ) / ( Gravity * TargetX ) )

Note that this formula assumes you are firing from (0, 0), so you'll have to offset the target x and y accordingly.

This gives you the 2 possible launch velocities (assuming it's possible to reach that point given the initial velocity). Note, wherever I used velocity previously, InitialVelocity is what it actually means.

Those are all the ones I feel like doing. If you need the other 2 (and I'm NOT getting into air-resistance), I might try.
NOTE: All of the code here is untested. It may or may not work.

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