The trajectory of a ball can be computed withwhere y = the height (m), θ0 = the initial an...

The trajectory of a ball can be computed with

where y = the height (m), θ₀ = the initial angle (radians), υ₀ = the initial velocity (m/s), g = the gravitational constant = 9.81 m/s², and y₀ = the initial height (m). Use the golden-section search to determine the maximum height given y₀ = 2 m, υ₀ = 20 m/s, and θ₀ = 45°. Iterate until the approximate error falls below ε_s = 10% using initial guesses of x_l = 10 and x_u = 30 m.