15) Have the user input the altitude of the airplane, h. Then write to the Comma

Question

15) Have the user input the altitude of the airplane, h. Then write to the Command Window the same text in the answer section, which used h = 900 ft as in the example. Note: underline values should be the values of appropriate variables entered or calculated.

15. An airplane is flying at a height of 900 ft while watching a target that is 70 ft tal (H- 70 ft), as shown in the igure. Tbe best view of the target is when 0 is maximum. Write a MATLAB program that detemies the distance x at which 0 is maximum. Define a vector x with elements ranging from 50 to 1500 with spacing of 0.5. Use this vector to calculate the corresponding values of 0. Then use MATLAB's built-in func- tion max to find the value of x that corresponds to the largest value ofe.

Explanation / Answer

in the above figure

angle X = tan-1(x/h)

angle Y = tan-1( x / (h-70) )

hence Theta = Y - X = tan-1 (x/h) - tan-1 (x/ (h-70) )

matlab program:

h=input('enter the height:');%reading height
x=50:0.5:1500;%creating x vector from 50 to 1500 in steps of 0.5
theta = atand(x/(h-70)) - atand(x/h);% finding theta for each value of x
max_theta = max(theta)% finding maximum value of theta
x_for_max_theta = x(find(theta == max_theta)); % finding x value corresponding to max value of theta
fprintf("value of x that give maximum value of theta = %f is %f ",max_theta,x_for_max_theta);

Output:

enter the height:900   

max_theta =  2.3190

value of x that give maximum value of theta = 2.318959 is 864.500000

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