Problem 3-9 - Vector sum - Part 9 (c)
Find the magnitude and direction of the sum of the vectors \(A + B + C\) using the component technique. Assume two significant digits.
\(A = 20\; km\) north, \(B = 30\; km\) east, \(C = 50\; km\; 55 ^\circ\) west of north.
Accumulated Solution
| Variable | \(x\) comp | \(y\) comp |
|---|---|---|
| A | \(0\) | \(+20\) |
| B | \(30\) | \(0\) |
| C | \(-50 \cos 35^\circ = -41\) | \(50 \sin 35^\circ = 28.7\) |
| Sum | \(30 - 41 = -11\) | \(20 + 28.8 = 48.7\) |
Correct!
\(\tan \theta = |R_y|/|R_x| = 48.7/11 = 4.43\)
\(\text{Therefore}\; \theta = 77^\circ\)
\(\text{Therefore the sum of A} \; = 20\; km\; N, B = 30 \;km E\; \text{and} \; C = 50\; km \;55^\circ \;W\; \text{of } \;N\; \text{is} \\
R = 50\; km\; 77^\circ \; N\; \text{of} \; W.\)
You have completed this problem.