Finding length of an arc produced by projectile

[sk0071]

So I decided to try deriving a general formula for fun. Being a high school student, the calculus got scary very fast. At this point, I'm just curious as to what the best approach to this might be. The approach I used was finding y as a function of x and then inputting it into the arc length formula. I eventually derived a very complicated formula that I think is wrong. I don't know very much about calculus as everything I've learned about it I've learned through the internet. Would this approach work? Is there a better way? If so what is the correct formula?

 

[PeroK]

You should post what you've done as homework. It's not possible to help without seeing what you've done.

 

[mathman]

Arc length question is best posed as a math question - not physics.

 

[Baluncore]

An ideal ballistic projectile would move along an inverted parabola. Parabolas are usually friendly, but the arc length of a parabola does become surprisingly complicated, but it is still soluble using arc length formula. You are probably on the right trajectory.

https://en.wikipedia.org/wiki/Parabola#Length_of_an_arc_of_a_parabola