Chapter 8, Problem 37P

Aerospace engineers sometimes compute the trajectories of projectiles like rockets. A related problem deals with the trajectory of a thrown ball. The trajectory of a ball is defined by the $\left(x,y\right)$ coordinates, as displayed in Fig. P8.37. The trajectory can be modeled as

$y=\left(\text{tan }{\theta }_0\right)x-\frac{g}{2v_0^2{\text{ cos}}^2{\theta }_0}{x}^2+y_0$

Find the appropriate initial angle ${\theta }_0$, if the initial velocity $v_0=20\text{m}/\text{s}$ and the distance to the catcher x is 40 m. Note that the ball leaves the thrower's hand at an elevation of $y_0=1.8$m. and the catcher receives it at 1 m. Express the final result in degrees. Use a value of 9.81 $\text{m}/{\text{s}}^2$ for g and employ the graphical method to develop your initial guesses.

FIGURE P8.37