Shooting projectiles given an angle and power

Question

I'm doing a prototype game like Worms and I would like not only to shot, but also see the whole projection curve where my shot will travel before it hit the ground. The only information given by the player is an angle and a power. There is also some level elements like wind and gravity.

Can I have a code for the projection curve? its like a parabola I think. I research about parabola but I had some difficult to apply these math formulas into the programming code.

Thanks.

Answer 1

The math (and physics) part

So this seems like 10th grade physics to me.

The path trced by a projectile is (as you said) a parbola describable by the equation

Now, if you solve this equation, you get the following parameters:

Range:

Height:

(vi = initial velocity, theta i = initial angle of shooting wrt horizontal)

And, the equation in (x, y) for the parabolic path will be

(v0 = initial velocity, theta = firing angle)

The programming part

assuming the following constants:

const g:Number = 9.81; //9.81 m/s, the grav const

The sin function is available as Math.sin

The power function is available as Math.pow. This means, sine squared will be

Math.pow(Math.sin(theta), 2)

You could write the range function as

function projectileRange(vel:Number, angle:Number):Number {
    var vsquare:Number = vel * vel;
    var rv:Number = vsquare * Math.sin(2 * angle) / g;
    return rv;
}

and the height function as

function projectileHeight(vel:Number, angle:Number):Number {
    var vsquare:Number = vel * vel;
    var rv:Number = vsquare * Math.pow(Math.sin(angle), 2) / (2 * g);
    return rv;
}

and the yPosition function as

function yPosition(xPos:Number, vel:Number, angle:Number):Number {
    return xPos * Math.tan(angle) - (g * xPos * xPos / (2 * vel * vel * Math.cos(angle) * Math.cos(angle)));
}

Note that the angles are in RADIANS

function toRadians(degrees:Number):void {
    return degrees * Math.PI / 180;
}

For more information on projectile motion, google it.