Question

19 klaus is riding his bicycle, heading directly north. he bikes north for 3.8 km, then turns west and bikes west for 2.2 km. what is the direction of klaus resultant displacement vector?
27° north of west
30° west of north
27° west of north
30° north of west

Explanation:

Step1: Analyze the displacement components

Let the north - ward displacement be \(y = 3.8\mathrm{km}\) and the west - ward displacement be \(x=2.2\mathrm{km}\).

Step2: Calculate the angle using trigonometry

We use the formula \(\tan\theta=\frac{x}{y}\) (where \(\theta\) is the angle west of north).
Substitute \(x = 2.2\) and \(y = 3.8\) into the formula: \(\tan\theta=\frac{2.2}{3.8}\approx0.579\).
Then \(\theta=\arctan(0.579)\approx30^{\circ}\)

Answer:

\(30^{\circ}\text{ west of north}\)