Abstract
The derivation of the maximum projection angle in projectile motion of a particle gives one of the most popular examples in elementary mechanics. This procedure is also a typical example of optimization problem although it has not been emphasized in many textbooks of mechanics. We formulate the problem on the basis of the optimization approach, and obtain the perturbed solution in terms of aerodynamic parameters. This solution yields the optimum angles in the following three examples: simple projection with vertical displacement between launch and landing positions, projection with initial speed depending on initial angle and also projection under the action of fluid dynamic forces such as drag and lift proportional to flight speed. These results show realistic angles in several projection phenomena appearing in our usual life, and successfully explain the mechanism. This fact means the significance of optimization approach in elementary mechanics, and it will be effective to introduce this concept to early education in mechanics.
