The equations of motion can be combined algebraically to yield an equation to determine the height of the ball, y , as a function of x and the initial conditions of the ball's release (height, h, initial speed v0 and the angle of release θ) :
The parameter g = 32.2 ft/s^2 is the acceleration due to gravity. Write a "quarterback calculator" function that outputs the required angle(s) of release given an input vector of one or more throwing velocities (initial speeds) and the location ( x , y) of the target down field. The function should accept the following inputs (in order): 1.A vector of one or more throwing velocities ( v0 ) in feet/second 2.The height of release ( h ) in feet 3.The distance down field to the receiver ( x ) in feet 4.The height of the target catch ( y ) in feet 5.An initial guess for the numerical solution of θ in degrees 6.A stopping criterion for the numerical solution
Your function should use fzero along with the input numerical guess and stopping criterion to solve for the angle of release ( θ ) corresponding to each value in the input vector of release velocities. Your function should have two outputs (in order): 1.A column vector of release angles ( θ ) in degrees corresponding to each value in the input vector of initial speeds. 2.A column vector of residual values associated with the numerical solution for each release angle.
