Aerospace engineers sometimes compute the trajectories of projectiles like rockets. A related problem deals with the trajectory

Question:

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 ?₀) x ? g/2v²₀ cos² ?₀ x₂ + y₀

Find the appropriate initial angle ?₀, if the initial velocity ?₀ = 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.