Static Problem: Please answer part A, B, and C. Geometric and Component Vector A

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Static Problem: Please answer part A, B, and C.

Geometric and Component Vector Addition Learning Goal: To use geometric and component addition of vectors Four vectors A, B, C, and D are shown (not to scale). Vector A has magnitude 23.9 and acts at an angle of 13.3 degrees with respect to the positive x axis. Vector Bhas magnitude 13.1 and egrees with respect to the positive xaxis. Vector C magnitude 47,3 ang nd acts at an angle of 1467 degrees with respect to the positive x axis, Vector D has magnitude 15.0 and acts at an angle of 295.3 degrees with respect to the positive Xaxis Figure 1 Part A Geometric addition What are the magnitude and direction of the resultant vector, R, when the parallelogram lawis applied to A and B? Express the magnitude to three significant figures. Express the angle to one decimal place, measured counterclockwise from the positive x axis. Separate your answers by a comma. R- 34.8.0.119 R,0. Submit incorrect; Try Again: 11 attempts remaining Term 1: Not quite. Check through your calculations, you may have made a rounding error or used the wrong number of significant figures. Part B. Component addition of vectors What is the resultant vector, R, obtained by adding vectors Cand D? Express the magnitude to three significant figures. Express the angle to one decimal place, measured counterclockwise from the positive Xaxis. Separate your answers by a comma. R,0. Part C Addition of more than two vectors Now wish to add all four vectors. Attempting to do this using the parallelogram method is difficult because that method is optimized for two vectors. It is much easier to use vector components when there are more than two vectors being added For the vector sumR A+B+C+ D, what are the magnitude and direction of the resultant R? Express the magnitude to three significant figures. Express the angle to one decimal place, measured counterclockwise from the positive x axis. Separate your answers by a comma. R 45.0, 1.29 R,0. Submit Hints M Answers incorrect; Try Again: 10 attempts remaining Provide Feedback Continue

Explanation / Answer

a)Ax+Bx = Rx and Ay+By = Ry

where, Ax = A*cos(thetaA)

putting values, we get

Rx = 28.14 and Ry = 17.65

Now, R = square root of( Rx^2 +Ry^2)

=> R = 33.223,

and angle = tan inverse of (Ry/Rx)

angle = 32.096 degrees

or R = 33.2 and angle = 32.1 degrees

b) solving the same procedure of part a), we get

R1 = 35.371

theta1 = 159.46

or R1 = 35.4m and theta1 = 159.5 degrees

c) now we have to calculate vector sum of all 4 vectors,

Let, S = A+B+C+D = R+R1

solving it similar to part a)

=> magnitude of S = 30.472 or 30.5m

and theta2 = 99.4 degrees

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