1. The problem statement, all variables and given/known data Use energy conservation to answer the following question. A mass is attached to one end of a massless string, the other end of which is attached to a fixed support. The mass swings around in a vertical circle as shown. Assuming that the mass has the minimum speed necessary at the top of the circle to keep the string from going slack, at what location should you cut the string so that the resulting projectile motion of the mass has its maximum height located directly above the center of the circle? 2. Relevant equations kinetics, energy conservation 3. The attempt at a solution The speed at the top of the circle is sqrt(rg). The energy at the top of the circle is E=1/2mrg+2rmg=5/2mrg, given we take 0 as the bottom of the circle. e=(Ke+Pe). The energy is conserved around the system, so choose another point a; Ea=Etop.... 5/2mrg=1/2mv^2+mg(r+rcosx).... then v= sqrt(rg(3-2cosx). If the max height did not need to be at the top of the circle, the angle would be 90. I tried to deal with this condition by, x-dir: d=vt, then t=rsinx/(sqrt(rg(3-2cosx))cosx. This yields an unwieldy derivative when I try to maximize distance in the y-direction. I've done a lot of useless math on this one. Please help!