Meriam, Kraige & Bolton — Kinematics of Particles: Problem 2_214

*2/214 A particle $P$ is launched from point $A$ with the initial conditions shown. If the particle is subjected to aerodynamic drag, compute the range $R$ of the particle and compare this with the case in which aerodynamic drag is neglected. Plot the trajectories of the particle for both cases. The acceleration due to aerodynamic drag has the form $\mathbf{a}_D = -kv^2\mathbf{e}_t$, where $k$ is a positive constant, $v$ is the particle speed, and $\mathbf{e}_t$ is the unit vector associated with the instantaneous velocity $\mathbf{v}$ of the particle. The unit vector $\mathbf{e}_t$ has the form $\mathbf{e}_t = \frac{v_x\mathbf{i} + v_y\mathbf{j}}{\sqrt{v_x^2 + v_y^2}}$, where $v_x$ and $v_y$ are the instantaneous $x$- and $y$-components of particle velocity, respectively. Use the values $v_0 = 65 \text{ m/s}$, $\theta = 35^\circ$, and $k = 4.0 \times 10^{-3} \text{ m}^{-1}$.