Modeling the linear drag on falling balls via interactive fuzzy initial value problem

Abstract

In this paper, we consider the linear drag of a falling ball, which can be well described using an interactive fuzzy initial value problem. The solution of the interactive fuzzy initial value problem gives us two types of solutions. One solution is when the uncertainty increases as time evolves, that is to say when the diameter of the fuzzy velocity increases exponentially. Hence, we ignore this solution, because we cannot expect this type of behavior for a ball that drags on a specific fluid. After all, experimentally, the ball must reach a well-known terminal velocity. The other branch of solution behaves as expected, the time-dependent fuzzy velocity converges to a well-known terminal velocity; meaning that, the diameter of the fuzzy velocity converges to terminal velocity. Therefore, we explore several conditions of fuzzy initial velocity and conclude that, for any fuzzy initial velocity, the fuzzy terminal velocity always converges to the classical terminal velocity, which is well known in the literature. We also present the corresponding time-dependent fuzzy acceleration, which becomes null for a sufficiently long time.