The equations of motion can be combined algebraically to yield an equation to de

Question

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 ) : 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): A row vector of one or more throwing velocities ( v0 ) in ft/s The height of release ( h ) in ft The distance down field to the receiver ( D ) in ft The height of the target catch ( y ) in feet An initial guess for the numerical solution of in degrees Your function should use fzero along with the input numerical guess to solve for the angle of release ( ) corresponding to each value of the throwing velocity. Your function should have the following output: A row vector of release angles ( ) in degrees corresponding to each value of the input throwing velocity (also in row vector form). Note: The first test case is for a single release velocity, so you can make sure your function works for only scalar inputs before modifying it to solve for a vector of initial speeds. 60.*tan(theta)+57960./v0.^2+6 need to be written up in matlab code with v0 varying from 45:60

Explanation / Answer

Make a vector t with times that the ball will be in the air, with the last number being the longest you might ever expect it to be in the air:

Then get equation for height:

Then plot it

when it hits the ground (h=0) using fzero.

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