Four vectors A, B, C, and D are shown (not to scale). Vector A has magnitude 20.

Question

Four vectors A, B, C, and D are shown (not to scale). Vector A has magnitude 20.7 and acts at an angle of 15.1 degrees with respect to the positive x axis. Vector B has magnitude 12.7 and acts at an angle of 70.3 degrees with respect to the positive x axis. Vector C has magnitude 38.3 and acts at an angle of 145.3 degrees with respect to the positive x axis. Vector D has magnitude 13.0 and acts at an angle of 290.1 degrees with respect to the positive x axis.

Now we 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 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 counterclockwise from the positive x axis. Separate your answers by a comma.

Explanation / Answer

A = 20.7 ( cos15.1i + sin15.1 j)

A = 20i + 5.39j   

B = 12.7 ( cos70.3i + sin70.3j)

B = 4.28i + 12j

C = 38.3 ( cos145.3i + sin145.3j)

C = -31.5i + 21.8j

D = 13 (cos290.1i + sin290.1j)

D = 4.47i - 12.2j

R = A + B + C + D

R = - 2.75i + 27j

Magnitude = sqrt(2.75^2 + 27^2) = 27.1 ..........Ans

angle = 180 - tan^-1(27 / 2.75) = 96 deg ......Ans

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.