I'm having trouble with this physics question: A 20kg sphere is hanging from a hook by a thin wire 3.50m long, and can swing in a complete circle. It is struck horizontally by a 5kg steel dart that embeds itself in the sphere. What is the minimum speed of the dart such that on contact it causes the combination to make one circular loop? This seems very much like a ballistic pendulum question but I can't seem to get the correct answer. I assumed that if the pendulum managed to reach the apex of its trajectory (in which it would be diametrically opposite from the rest point), then the force of gravity would bring it back, completing the circle. That didn't work. What am I doing wrong? The ballistic pendulum equation, by the way, is v=(m+M/m)sqrt(2gy), where m is the mass of the moving dart and M the mass of the motionless sphere.