Science Puzzle
The Sliding Pucks
Two pucks start at the same high point. Track A is a straight diagonal line to the finish. Track B curves steeply downward first, then levels off to the same finish point. Both tracks cover the same vertical drop.
Both pucks are released at the same instant with no initial push. Which reaches the finish line first?
The Answer
Track B wins. The shorter path is not always the faster one.
On Track B, the puck encounters the steep section first. It accelerates quickly and gains high speed early. Although the horizontal section adds distance, the puck is now moving fast enough to cover it quickly.
On Track A, the puck accelerates more gradually along the slope. It never reaches the same peak speed before the finish.
The shape that minimises travel time between two points under gravity is called a brachistochrone, from Greek meaning "shortest time". Counterintuitively, it is not a straight line but a specific curve (a cycloid). This was one of the first problems in the calculus of variations, solved in 1696 by Johann Bernoulli and independently by Newton, Leibniz and others.
The principle: The brachistochrone problem. The fastest path between two points under gravity is not a straight line but a curve that accelerates quickly early. Speed gained early more than compensates for the longer distance.