find the north and east components of the displacement (in km) for the hikers shown in the figure below…

Explanation:

Step1: Find north - component formula

The north - component of a vector $\vec{S}$ with magnitude $S$ and angle $\theta$ with the x - axis is given by $S_y=S\sin\theta$.

Step2: Calculate north - component

Here, $S = 2.90$ km and $\theta = 40^{\circ}$. So, $S_y=2.90\sin40^{\circ}$. $S_y=2.90\times0.6428\approx1.86$ km.

Step3: Find east - component formula

The east - component of a vector $\vec{S}$ with magnitude $S$ and angle $\theta$ with the x - axis is given by $S_x = S\cos\theta$.

Step4: Calculate east - component

$S_x=2.90\cos40^{\circ}$. $S_x=2.90\times0.7660\approx2.22$ km.

Answer:

north component: $1.86$ km east component: $2.22$ km