The three displacement vectors in the drawing have...

The three displacement vectors in the drawing have magnitudes of A = 4.54 m, B = 6.95 m, and C = 4.47 m. Find the resultant ((a) magnitude and (b) directional angle) of the three vectors by means of the component method. Express the directional angle as an angle above the positive or negative x axis.

Transcript

00:01 Hi, here this given problem is based upon the component method of vector addition.

00:10 In it there are three displacement vectors are given in x, y, plane.

00:20 These are the x and y -axis.

00:23 This is the first of the displacement vector vector a.

00:31 This is in the second quadrant having a magnitude of 4 .54 meter and making an angle 20 .0 degree from the negative x -axis.

00:49 Another displacement vector that is vector b at an angle of 60 degree and having a magnitude of 6 .95 meter at an angle 60 .0 degree with the positive x -axis and the third one, third displacement vector that is vector c along negative y -axis.

01:19 So this is a, a bar, this is b bar, and this is c bar having the magnitudes, a is equal to 4 .54 meter, b is equal to 6 .95 meter and c is equal to 4 .47 meter.

01:44 In the first part of the problem we have to find magnitude of the resultant for which, first of all, we resolve the given vector along x -axis and y -axis.

01:56 So first of all, horizontal component along x -axis of this vector a, as it will be along negative x -axis, so this will be represented as minus.

02:09 So this is minus a cost 20 degree.

02:13 Means this is minus 4 .54 meter into cosine of 20 degree and it is calculated to be equal to minus 4 .27 meter then along y -axis positive y -axis its component is that will be given by plus a a is 4 .54 meter into sine 20 degree and it comes out to be equal to 1 .55 meter then we resolve this b it will also be having two components and both the components will be positive along positive x -axis and along positive y -axis so b x will be equal to b cos 60 degree means this is 6 .95 into cos 60 degree and it is calculated to be equal to plus 3 .475 meter and its vertical component b y that is plus b sine 60 degree means this is plus 6 .95 meter into sine 60 degree and it is calculated to be equal to plus 6 .0 to meter and finally the third one that is only having the component along y -axis as it is it itself is along negative y -axis so c y is equal to minus c means minus 4 .47 meter so net displacement along x -axis that will be given by a x plus a y means minus 4 .27 plus 3 .47 75 meter calculated to be equal to minus 0 .795 meter and along y -axis, ay plus b -y plus c -y means 1 .55 plus 6 .02 minus 4 .47 meter and it is calculated to be equal to 3 .1 meter...

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