I should know how to do this but I don't. I'm not very familiar with vectors. Perhaps I will be after this.
So I have a stream of water falling out of a pipe. It obviously forms a parabola of the form $f(x) = -ax^2+h$, where $h$ is the height of the pipe from the ground, $a$ is some constant and $x$ is the horizontal distance from the pipe.
The question is: if I know $h$, and I know at what distance the water hits the ground, what is the initial speed of the water as it exits the pipe, assuming that it exits the pipe parallel to the ground?
I'm going to try to figure this out myself, but I'd like to return to see how you guys solve this. (btw, not a homework question. I'm 30 years old and just curious.)