In this video
Khan academy explains conservation of energy for a falling object. He looks at an object falling perpendicularly from height h and computes its velocity at height zero. So far so good. But then he draws a curve that has several variations in height such that the object needs to climb back to certain height before falling back. At the end he computes again the velocity of the object and finds the same as object falling on the perpendicular.
Intuitively this seems wrong to me. To simplify his drawing I drew this picture:
I reason like this: The object falls to C but then it needs to climb back up to D and at D its vertical velocity is zero (because it changes direction, but not sure if this correct). So at B the velocity will be as if the object fell from D not from E. Is this correct? What is the best way of thinking about this problem?