Racing Blocks

The motions animated here are in a vertical plane and are imagined to be taking place on smooth surfaces. This applet brings out the importance of the need to look for the components of vectors in understanding motion. The body moving along the curved path has a greater horizontal component of velocity at all points of the curve as compared to the the body moving along the straight path. This explains why the body traveling the longer path arrives at the original height earlier than the one traveling the shorter straighter path. The show button doubles as hide button too. It allows placing of dots at the position of the blocks  at regular intervals of time. The path between two points in the gravitational field that takes least time is a segment of a cycloid. It is known as brachistochrone [brachistos - "shortest" and chronos - "time"]