PartA) What are the magnitude and direction of the resultant vector, R , when th
ID: 1878982 • Letter: P
Question
PartA) What are the magnitude and direction of the resultant vector, R, when the parallelogram law is applied to A and B?
Geometric and Component Vector Addition 1 of 2 X Incorrect; Try Again Learning Goal: To use geometric and compenent addilion of vectors. Four vectors A, B, C, and D are shown (not to ecale). Vector A has magnitude 21.9 and acte at an angle ol 14.1 degrees with respect to the poeitive x axis. Vector B has magnitude 12.3 and acts at an angle of 70.9 degrees with re8pect to the positive x axi8Vector C has magnitude 28.3 and acts at an angle of 147.9 degrees with respect to the positive x axis. Vector D has magnitude 14.0 and acts at an angle of 202 3 degrees with respect to the positive x axis, Part B-Component addition of vectors What is the rasuant vector, R, obcained by adding vectors C and D 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 View Available Hint(s) Figure 1) Submit Part C-Addition of more than two vectors Now ws wish to add all four vectors. Attampting to do this using the paralelogram mathod is ditficult because that method is optimized for two veciors. it is much easier to use vector components when thers are more than two vectors being added For the vector sum R-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 counterclock tse from the positive axis. Separate your answers by a Figure 1 of 1 View Available Hint(s) Submit Provide Feedbaclk Next >Explanation / Answer
A = 21.9 ( cos14.1i + sin14.1j) = 21.24i + 5.34 j N
B = 12.3 ( cos70.9 i + sin70.9 j) = 4.025i + 11.62 j
C = 28.3(cos147.9i + sin147.9j ) = -23.97i + 15.04j
D = 14(cos292.9i + sin292.9j) = 5.448i + -12.897 j
(A) R = A + B = (21.24+ 4.025)i + (5.34 + 11.62)j
R = 25.265i + 16.96 j
magnitude , |R| = sqrt(25.265^2 + 16.96^2) = 30.4
direction = tan^-1(16.96 / 25.265) = 33.9 deg
Ans: 30.4, 33.9
(B) R = C + D = - 18.522i + 2.143 j
|R| = 18.6
theta = 180 - tan^-1(2.143/ 18.522) = 173.4 deg
Ans: 18.6, 173.4
(C) R = A + B + C + D = 6.743i + 19.103 j
|R| = 20.2
theta =70.6 deg
Ans: 20.2, 70.6