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In polar coordinates a two-dimensional vector is given by its radius and angle (

ID: 3796788 • Letter: I

Question

In polar coordinates a two-dimensional vector is given by its radius and angle (r, theta). Write a user- defined MATLAB function that adds two vectors that are given in polar coordinates. For the function name and arguments use [r th] = AddVecpol(r1, th1, r2, th2), where the input arguments are (r_1, theta_1) and (r_2, theta_2), and the output arguments are the radius and angle of the result. Use the function to carry out the following additions: r_1 = (5, 23degree), r_2 = (12, 40degree) r_1 = (6, 80degree), r_2 = (15, 125degree) The fuel efficiency of an automobile is measured in mi/gal (miles per U.S. gallon) or in km/L (kilometers per liter). Write a MATLAB user-defined function that converts fuel efficiency values from km/L to mi/gal. For the function name and arguments use mpg= kmlTOmpg (kml). The input argument kml is the efficiency in km/L, and the output argument mpg is the efficiency in mi/gal. Use the function in the Command Window to: (a) Determine the fuel efficiency in mi/gal of a car that consumes 9 km/L. (b) Determine the fuel efficiency in mi/gal of a car that consumes 14 km/L

Explanation / Answer

The Matlab function AddVecPol.m

function [r,th] = addvecPol(r1,th1,r2,th2)
   r = sqrt(r1^2+r2^2+2*r1*r2*cosd(th2-th1)); % Computing r
   th = th1 + atan2d(r2*sind(th2-th1),r1+r2*cosd(th2-th1)); % Computing theta
end

Testing the function

>> r1 = 5;th1 = 23;
>> r2 = 12;th2 = 40;
>> [r,th] = addvecPol(r1,th1,r2,th2)

r =

   16.8451


th =

   35.0215

>> r1 = 6;th1 = 80;
>> r2 = 15;th2 = 125;
>> [r,th] = addvecPol(r1,th1,r2,th2)

r =

   19.7048


th =

112.5663

>>

Matlab function kmlTompg.m

function mpg = kmlTompg(kml)
   mpg = kml*2.35215; % Converting km/l to mil/gal
end

Testing th efunction

>> mpg = kmlTompg(9)

mpg =

   21.1694

>> mpg = kmlTompg(14)

mpg =

   32.9301