You throw a baseball at a 45 degree angle to the horizontal, aiming at a friend who's sitting in a tree a distance h above level ground At the instant you throw your ball, your friend drops another ball. (a) Show that the two balls will collide, no matter what your ball's initial speed, provided it's greater than some minimum value. (b) Find an expression for that minimum speed.
The Attempt at a Solution
I haven't attempted the problem mathematically yet, and I am sure I will be fine with that, but I am having trouble with it conceptually. I am assuming that the baseball I throw is meant to hit my friend, so assuming my aim is good, my ball will hit my friend, that is, it will be at a height h at some time t > 0, but if my friend drops a ball at the instant I throw my ball, then his ball is at a height less than h at the same time t that my ball is at height h. So how can the balls collide?