We want to design a ball throwing robot arm that will throw a ball with initial velocity V0at an angle θ to the ground plane. Assuming that the robot arm is at coordinates x= 0 the ball will hit the ground at xf= (Vo^2 * sin2θ)/g *** where g=9.8 m/s^^2 is the gravitational constant. We want to ensure that the ball hits the ground at xf= 0.1730861 meters. Unfortunately, we are not free to choose the necessary V0 and θ since the robot design constrains the speed to be a function of the angle as V0=k(1 + cosθ) where k= 0.75*** is a design parameter.
Calculated f is the translated version of this problem into a root finding problem, then bisection method solves it by searching for θ in the interval [0◦,40◦]
At the end also calculated V0 for the founded 0 value. Although the range is given in degrees, it performs the calculations in radians.
Calculating the x-coordinate of the intersection of the parabola ***y=−x^2 + 4.0 *** with the line y= 4x−1.0 starting from an estimate of x0= 1.5
f1 is the function y=−x^2+4.0 , findy is the function x = (y+1.0)/4; ,