Starting with an initial speed v0, a mass m slides down a curved frictionless track (a shown in the figure below), arriving at the bottom with a speed v. From what vertical elevation h did it start?

Answer 1

(PE+KE)initial = (PE+KE)final
mgh + mv0^2/2 = 0 + mv^2/2
=> h = (v^2-v0^2)/2g