Chapter 3, Problem 3.6P

A radar tracks the flight of a projectile (see Figure P3.6). At time t, the radar measures the horizontal component $v_x\left(t\right)$ and the vertical component $v_y\left(t\right)$ of the projectile’s velocity and its range $R\left(t\right)$ and elevation $\varphi \left(t\right)$ . Are these measurements sufficient to compute the horizontal distance D from the radar to the launch point of the projectile? If so, derive the expression for D as a function of g and the measured values $v_x\left(t\right)$ , $v_y\left(t\right)$ , $R\left(t\right)$ , and $\varphi \left(t\right)$ .