Problem 3-9 - Vector sum - Part 8 (b)
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!
Using the Pythagorean relation
\(R = (R_x{^2} + R_y{^2})^{1/2}= [(-11)^2 + (48.7)^2]^{1/2} = 50\; km\)
\(\theta \) is given by \(\tan \theta =\) :
(A) \(R_x + R_y\)
(B) \((R_x{^2} + R_y{^2})^{1/2}\)
(C) \(R_y/R_x\)