I asked my Physics teacher about this and he was stumped. He went to ask the other AP Physics teacher, and he too had no clue. So if you guys know how to do this, feel proud. You're smarter than my teachers anyway.... Imagine that there's a ball attached with a string, as shown in attachment. there is no initial tension in the string. assume that the string does not "give"; it does not stretch. one end is the ball, initially at rest; the other end of the string is at a fixed point (0,12). The larger semicircle is the path the ball will follow once it falls far enough. (I figured out the length of the string in my question using some calculus and simply drew a circle centered at (0,12) with that radius.) We've only learned when the ball always follows a perfect circular path, but in this scenario, it starts falling completely vertically until it is caught by the string. How do calculations with this work? How high does it go after falling and being caught by the string? what speed is it going at the instant tension becomes present in the string? what is the speed at the lowest portion of the arc? If you need some values, assume that the ball is only a point with mass of 1 kg. It starts 12 m above the ground (x axis). the length of the string is approximately 9.29357m. |g|=10 m/s/s i have studied energy including PE=mgh and KE=.5mv^2. but that's the extent of my knowledge on that topic. Thanks in advance.