C++ program to find the time of flight of projectile
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Answer:
Introduction
This article describes how to numerically solve a set of second order differential equations with initial conditions. Nyström modification of the fourth order Runge-Kutta method is explained first. Then the method is applied to two problems: to find the trajectory of a flying projectile and to calculate coupled oscillations of a mechanical system with two degrees of freedom. The article is intended as a continuation of my previous article about solitary differential equations.
Background
Many textbooks bring a simplified approach to the calculation of a flying projectile's path. The simplification is based on the assumption that the horizontal and vertical components of projectile motion are independent and can be treated separately. This enables the setup of two equations of motion: one for the vertical throw under the force of gravity and the other for the horizontal motion with no acceleration, which keeps that velocity constant. Each of these two equations can be solved individually yielding quite realistic results.
Observing the situation more closely, however, we find that some tie between the horizontal and vertical movements should exist. The reason is aerodynamic drag. For velocities higher than, say, 20 km/h, the drag of a moving body is proportional to the square of the velocity. If we suppose that the drag works directly against the velocity direction, then the square dependency causes coupling of the horizontal and vertical forces that act on the projectile
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