A circular hoop of radius is stood vertically on a flat surface and held in place. A smooth wire is tightly stretched between the upmost point of the hoop and a point on the hoop at height ℎ. A bead of mass is held at rest at the top of this wire, upon which it is threaded.(Ignore air resistance)
Is it possible to use conservation of energy to solve find time taken? Start with the following energy relationship, $$ mg(2r)=mgh+\frac{1}{2}mv^2$$ Then solving for v, $$v=\sqrt{4gr-2gh}$$ As this is the velocity at the final point, this should be usable in a suvat, where a=g, u=0. $$v=u+at$$ $$t=\frac{v}{a}$$ $$t=\sqrt{\frac{4r-2h}{g}}$$ The suggested method is to use kinematics only, but I don't see why mine is not correct.