Projectile motion arc length of the trajectory using parametric equations. Parametric arc length.
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Arc length using parametric curves: projectile motion arc length of a trajectory problem. Find the arc length of the trajectory using parametric equations.
We start by finding the standard equations for the vertical and horizontal motion of a projectile by applying kinematics equations for each coordinate. Because these equations independently give the x and y coordinates as a function of time, they are actually a set of parametric equations for the trajectory of the projectile.
We quickly derive a formula for computing arc length with parametric equations, then we set up an integral for the arc length of the trajectory. To compute the arc length of the trajectory, this integral can be computed analytically using trigonometric substitution, but we opt for a numerical approximation using quad_qag in wxMaxima since we are already using decimal approximations in the arc length of parametric curves calculation.
