CYCLOIDS FOR MINIMAL TIME PROJECTION

Abstract

The minimum time has historical importance in relation to Fermat’s principle, a famous problem that is well known to the readers of general physics mattrers. Our intention in this study is to restrict ourselves to classical Newtonian mechanics, more specifically to a projectile mothion that every college student has certain familiarity. This study established and utilises the Brachistochrone general equation to investigate the minimum time curve travelled by an object (jet) under the influence of gravity. It was found that reaching a maximum altitude within the shortest time possible, a jet fighter must take off with the same speed at a smaller projection angle. This means that travelling directly against gravity takes more time.