This is a tough question. I'd like to know if anybody can find a good solution. It isn't required for any of my classes, but I'd like to see a theoretical result. It seems like it should be a simple projectile motion problem, but it's not that easy. Let's say there's a building x1 meters away and y1 meters tall. So, we only know x and y. What is the minimum initial velocity at which a projectile can be launched to "land" on top of this building? Assume that the projectile is launched from the origin. Obviously, we know the standard projectile equations. We know the x-distance and y-distance we must travel. We know how to convert vinitial to vx and vy. But how do we find the minimum vinitial and its corresponding theta? Any help would be appreciated.