Question

a car is driven east for a distance of 50km,then in a direction 30 degrees east of north for 25km.sketch the vector diagram and determine
(a) the magnitude and (b) the angle of the total displacement from its starting point.

Answer 1

a)

$$\begin{array}{l} \vec {S} = \vec {A} + \vec {B} \quad S = \sqrt {A ^ {2} + B ^ {2} - 2 A B \cos (9 0 {}^ {\circ} + 3 0 {}^ {\circ})} \\ = \sqrt {5 0 ^ {2} + 2 5 ^ {2} - 2 * 2 5 * 5 0 \cos (9 0 {}^ {\circ} + 3 0 {}^ {\circ})} = 6 6 \mathrm {k m} \\ \end{array}$$

b)

$$B ^ {2} = A ^ {2} + S ^ {2} - 2 A S \cos \theta$$ $$\cos \theta = \frac {A ^ {2} + S ^ {2} - B ^ {2}}{2 A S} = \frac {5 0 ^ {2} + 6 6 ^ {2} - 2 5 ^ {2}}{2 * 5 0 * 6 6} = 0, 9 4 4 \quad \rightarrow \theta = 2 0 {}^ {\circ}$$