Ballistic trajectory, can't isolate angle

[Nico-M]

Hey guys,

I constructed a function that describes the ballistic trajectory of an object with a given velocity and angle. This is what it looks like:
$$y=tan(a)x+gx^2/(2(cos(a)v)^2)$$
'x' and 'y' are the x- and y-positions of the object in flight.
'v' is the velocity and 'a' the angle in degrees at which the object is thrown/launched.
'g' is the gravitational acceleration that causes the object to travel in an arc.

What I'd like to be able to do with this function is to calculate at which angle the object will strike a given (x,y)-position with a given velocity. For this I had to isolate the angle-variable...well I tried to. I wrote down all the algebra I could think of but I just can't figure out how to isolate that angle with all those sines and cosines in the way. Not very experienced with these yet...

I hope someone can help me out with this one, and step-by-step instructions would be awesome!

 

[coelho]

Well... for calculating what you want, you will need to know (or learn) the bit of calculus called derivatives. If you know it already, the angle you are searching for is given by:

$$tan(a)=\frac{dy}{dx}$$

where dy/dx is the derivative of the y function you got.

If you don't know how to calculate (or even what are) derivatives, i fear you will have to learn it first to be able to understand this.