Question

find the north and east components of the displacement (in km) from san francisco to sacramento shown in the figure below. north component km east component km

Explanation:

Step1: Recall vector - component formula

For a vector of magnitude $S$ at an angle $\theta$ with the x - axis (east - direction here), the x - component (east - component) is $S_x = S\cos\theta$ and the y - component (north - component) is $S_y=S\sin\theta$.

Step2: Identify values of $S$ and $\theta$

We are given that $S = 123$ km and $\theta = 45^{\circ}$.

Step3: Calculate the north - component

$S_y=S\sin\theta=123\times\sin45^{\circ}=123\times\frac{\sqrt{2}}{2}\approx123\times0.707 = 86.961$ km.

Step4: Calculate the east - component

$S_x=S\cos\theta=123\times\cos45^{\circ}=123\times\frac{\sqrt{2}}{2}\approx123\times0.707 = 86.961$ km.

Answer:

North component: $87.0$ km (rounded to one decimal place)
East component: $87.0$ km (rounded to one decimal place)