To be fair it's harder to figure it out by inspection. (More or less because one thing you've specified is important - the angle is locked in.)
Intuition tells me that usually if there's an ascent and descent possibility, the relevant quadratic you need to solve should yield two distinct positive solutions. It further tells me that if one thing ends up being negative, usually the ascent possibility is ruled out. (Usually the ascent-possibility corresponds to the negative square root when doing any quadratic formula stuff, and the positive square root corresponds to the descent.)
But of course, this kind of intuition could easily be wrong, and I'd be happy to accept otherwise if you did find some counterexample. That's what I'd gather though, personally.
Hi RuiAce
Sorry it took a while, I couldn't find the right question so I made up my own, hence the weird/convenient numbers.
(See Attachment)I made sure that there are no contradictions in any value (unlike most textbooks
), so no need to worry on that end.
The question has exactly the same amount of information as the one in this post, with the key difference being where the ball hits the castle on its path.
Since there is only one y value for each x value, there can only be
one possible time for this occurence. This means that a quadratic will never form to give more than one positive value, as there can only be one time and one x value at this point. (hence always a plus and minus if it's a quadratic).
I don't quite understand what you said about the negative answer in the quadratic ruling out the ascending case, as I have not yet seen anything logical that may suggest this to be the case.
The converse is obviously not true though. One y value can take on (up to) 2 x values due to the symmetrical shape of the parabola.
A quadratic would form when you solve for the height, y, being 20m, which you will get 43.017m for x at 0.993s (ascend) and 177.908m at 4.019 seconds (descend).
The fact that you know where the castle is (x) helps you find out whether the ball will collide with it during its ascension or descension, from my observation.
Thanks for reading, again.