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 (x, y) coordinates, as displayed in Figure. The trajectory can be modeled as
y = (tan θ0) x – g/2v20 cos2 θ0 x2 + y0
Find the appropriate initial angle θ0, if the initial velocity υ0 = 20 m/s and the distance to the catcher x is 35 m. Note that the ball leaves the thrower’s hand at an elevation of y0 = 2 m and the catcher receives it at 1 m. Express the final result in degrees. Use a value of 9.81 m/s2 for g and employ the graphical method to develop your initial guesses.