Chapter 13, Problem 17P

The trajectory of a ball can be computed with

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

where $y=\text{the}$ height (m), ${\theta }_0=\text{the}$ initial angle (radians), $v_0=\text{the}$ initial velocity (m/s), $g=\text{the}$ gravitational $\text{constant}=\text{9}{\text{.81 m/s}}^2$, and $y_0=\text{the}$ initial height (m). Use the golden-section search to determine the maximum height given $y_0=1\text{m}$, $v_0=25$m/s and ${\theta }_0=50°$. Iterate until the approximate error falls below ${\epsilon }_s=1\%$ using initial guesses of $x_1=0\text{and}{x}_u=60$m.