Falling Body Motion in Time Scale Calculus

Abstract

The falling body problem for different time scales, such as ℝ, ℤ, hℤ, qℕ0, ℙc,d is the subject of this study. To deal with this problem, we use time-scale calculus. Time scale dynamic equations are used to define the falling body problem. The exponential time scale function is used for the solutions of these problems. The solutions of the falling body problem in each of these time scales are found. Moreover, we also test our mathematical results with numerical simulations.