Question

4 ariane is riding her motorcycle heading directly south. she drives south for 7.0 km, then turns west and drives west for 1.4 km. what is the direction of arianes resultant displacement vector?
16° south of west
11° west of south
11° south of west
16° west of south

Explanation:

Step1: Determine the sides of the right - triangle

Let the south - ward displacement \(y = 7.0\mathrm{km}\) and the west - ward displacement \(x = 1.4\mathrm{km}\).

Step2: Use the tangent function to find the angle

The tangent of the angle \(\theta\) (measured from the south direction towards the west) is given by \(\tan\theta=\frac{x}{y}\).
Substitute \(x = 1.4\) and \(y = 7.0\) into the formula: \(\tan\theta=\frac{1.4}{7.0}=0.2\).
Then \(\theta=\tan^{- 1}(0.2)\approx11^{\circ}\).

Answer:

\(11^{\circ}\text{ west of south}\)