The trajectory of a ball thrown by a right fielder as defined in the (x,y) coordinates...

 

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The trajectory of a ball thrown by a right fielder as defined in the (x,y) coordinates can be modeled as: y = x tan 180 x² + Yo 元 2v cos 180 where the angle at which the ball leaves the right fielder's hand is 0, = 22° , the initial velocity is v, = 52 mph, the distance between the right fielder and the catcher is 35 m, and the throw leaves the right fielder's hand at an elevation of 1.5 m. You must use g = 9.81 m/s? and the following conversion factors: 1 mile = 5280 feet and 1 meter = 3.28 feet. (a) Plot the function using the plot command in figure 1. Title the plot "MAE 284, Homework 3, Problem 1, Part a". Use the axis command to change the axis so that the x axis starts at 0 and goes to 35 meters and the y axis goes from 0 to 10 m. (b) If the catcher cannot reach above an elevation of 2 m, will she catch the ball? Use an fprintf statement to display the result (e.g. "The catcher can/cannot catch the ball"). (c) Compute the maximum height reached by the ball using each of the following methods. Use the fprintf function to print the result. For example, "The maximum height using goldmin is 19.0214618608 m". Display 10 digits to the right of the decimal point. i. Golden-section search (x; = 0, x, = 30, e, =2%) ii. Parabolic interpolation ( x = 10, x, = 20, x; 30, Max iterations = 3) i. MATLAB's fminbndwith the iterations displayed. Use the range 0 to the distance of the catcher. The trajectory of a ball thrown by a right fielder as defined in the (x,y) coordinates can be modeled as: y = x tan 180 x² + Yo 元 2v cos 180 where the angle at which the ball leaves the right fielder's hand is 0, = 22° , the initial velocity is v, = 52 mph, the distance between the right fielder and the catcher is 35 m, and the throw leaves the right fielder's hand at an elevation of 1.5 m. You must use g = 9.81 m/s? and the following conversion factors: 1 mile = 5280 feet and 1 meter = 3.28 feet. (a) Plot the function using the plot command in figure 1. Title the plot "MAE 284, Homework 3, Problem 1, Part a". Use the axis command to change the axis so that the x axis starts at 0 and goes to 35 meters and the y axis goes from 0 to 10 m. (b) If the catcher cannot reach above an elevation of 2 m, will she catch the ball? Use an fprintf statement to display the result (e.g. "The catcher can/cannot catch the ball"). (c) Compute the maximum height reached by the ball using each of the following methods. Use the fprintf function to print the result. For example, "The maximum height using goldmin is 19.0214618608 m". Display 10 digits to the right of the decimal point. i. Golden-section search (x; = 0, x, = 30, e, =2%) ii. Parabolic interpolation ( x = 10, x, = 20, x; 30, Max iterations = 3) i. MATLAB's fminbndwith the iterations displayed. Use the range 0 to the distance of the catcher.

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clear all clc v40 h18 x100 y1 g981 format long f inlinex... View the full answer