Hi.
I want to throw an object into a parabola.
If I had set all the starting points, the end points, the gravity, the weight of the object, would I know the angle of the point of launch?
You’ll know I’m bad at math when you see me asking this question.
Please let me know if there is a formula that makes it possible.
Thanks!
If you can get 3 points I’ll give you some theory that should lead you to a possible solution. By calculating the derivative of a function, you can get a formula that describes the gradient, and using arctan(gradient), you can get the angle.
Lets look at an example. Please use Desmos to see the graph
-x2 +1
Calculating the derivative of a polynomial is simple, just bring down the exponent, and subtract one from the exponent. Constants fall away. Google examples if you are unsure.
-2x describes the gradient of this graph. So if you want the gradient at the start of the parabola. Looking on desmos it would start at -1. -2(-1) is 2. so the gradient is 2 at -1. Arctan(2) will give you the angle. Make sure your calculator is in the correct mode, degrees.
Now since this is a parabola, it is reasonably simple to calculate it from 3 points. I will derive the formulas here.
Given (x0,y0),(x1,y1),(x2,y2)
The general parabola is b0+b1x+b2x2
We can rewrite it as f(x) = a0+a1(x-x0)+a2(x-x0)(x-x1), this is allowed.
By subbing in x0 we get, a0 = y0
By subbing in x1 we get a1 = (y1-y0)/(x1-x0)
By subbing in x2 you get a2 = (((y2-y1)/(x2-x1))-((y1-y0)/(x1-x0)))/x2-x0
By subbing in your points, you can calculate a0, a1,a2, and using the formula, you have your parabolic function.
And from that you can calculate it’s derivative.
Please note, there is possibly an easier way. This is just what I thought off the top of my head.
Hope that helps