Make sure that you use comments to indicate what question you are answering, to

Question

Make sure that you use comments to indicate what question you are answering, to describe the purpose of that question, and any commands that may need to be described.



1. Suppose a TV with height of 60 feet has been mounted onto a platform so that the bottom of the TV is 150 feet off the ground:















Viewing of the TV is optimum when has been maximized. Generate an array for distance from 60 to 350 feet at increments of 0.5 feet. Calculate in degrees for each of these distances. Determine the max value of theta and the position in the array where this value occurs. Use the position (index/subscript) of the maximum value and the array for distances to determine the best distance for viewing.





2. Write a short script to solve the system of linear equations:



1x + 2y + 3z = 366

4x + 5y + 6z = 804

7x + 8y = 351



3. Do the following matrix exercises:



a. Create a 10 X 15 matrix A of random numbers evenly (uniformly) distributed between 10 and 30.

b. Create a 15 X 10 matrix B of random numbers evenly (uniformly) distributed between 10 and 30.

c. Create a matrix C which is the inverse of A * B.

d. Extract the 3rd row of matrix C and store in array E.

4. The flight path of a projectile is dependent on the angle () that it is fired. This path can be separated into a horizontal and vertical distance as a function of time.

horizontal distance(t) = t * Vo * cos()
vertical distance(t) = t * Vo * sin() – ½ gt2

where Vo is the initial velocity, g is the acceleration due to gravity (9.8 m/s2), and t is time in seconds.

Using the subplot command, plot the following 4 plots in one figure:



a. Assuming a launch angle of 60 degrees and an initial velocity of 100 m/s, plot the horizontal distance the projectile traveled versus time (time on the x axis) for 0 to 30 seconds. Add title and label axes.

b. Assuming a launch angle of 60 degrees and an initial velocity of 100 m/s, plot the vertical distance the projectile traveled versus time (time on the x axis) for 0 to 30 seconds. Add title and label axes.

c. Plot the vertical distance (y axis) versus the horizontal distance (x axis). Add title and label axes.

d. Calculate new arrays for the vertical and horizontal launch distances assuming launch angles of 90, 45, and 60 degrees. Plot the vertical distance (y axis) versus the horizontal distance (x axis) for each of these angles. Use different line types to represent each angle. Add title, label axes, and a legend to identify the line types.







Make sure that you add comments at beginning of your *.m file that include comments before the set of commands for the problem that specify, what is the purpose of the problem, what input is used, what output is expected and what processing is required. (Input processing and output should be clearly specified!) You may also use comments to state what a command is supposed to due if you believe it is unclear.

ps: please let me know if these should be put seperately inorder to get the answer but to the best of my knowledge this is one question based on which a progame needs to be written.

Explanation / Answer

For question 1 % For question 1, we will first need to create an array for distance, % then to find theta for respective distance we will have to use, % theta = atan(210/distance) - atan (150/distance) % this is because atan(210/distance) corresponds to the angle of the bigger % triangle and atan(150/distance) corresbonds to the angle of the smaller % triangle.thus substracting the two gives us the theta we are looking for. % now that we have both distance and theta array we use [a,b] = max(x), % to find the max value of theta and its position. % then by using the colon operator to extract the respective location of % the distance array. Thus we have the best distance for viewing. % distance = 60:0.5:350; theta = atan(210.0./distance)- atan(150.0./distance); [a, b] = max(theta); theta_max = distance(:,236); fprintf('The maximum angle occurs when the viewer is at %6.2f feet of distance ',theta_max);

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