The magnitude of a force \(xi + 15j\) is 17N. Find the : (a) possible

Explanation

(a) \(F = xi + 15j\)

\(|F| = \sqrt{x^{2} + 15^{2}} = 17\)

\(x^{2} = 17^{2} - 15^{2} = 64\)

\(x = \pm \sqrt{64} = \pm 8\)

\(x = 8 ; x = -8\)

(b)

\(\tan \alpha = \frac{15}{8} = 1.875\)

\(\alpha = \tan^{-1} (1.875) = 61.9° \approxeq 62°\)

\(\tan \beta = \frac{15}{-8} = -1.875\)

\(\beta = \tan^{-1} (-1.875) = -61.9°\)

= \(180° - 61.9° = 118.1° \approxeq 118°\)

Directions of forces are 62° and 118° each with the positive x- axis.