a jogger runs 5.0 km on a straight trail at an angle of 60° south of west. what is the southern component of…

Explanation:

Step1: Identify the formula for component

To find the southern - component of a vector with magnitude $d$ and angle $\theta$ below the horizontal, we use $y = d\sin\theta$. Here, $d = 5.0$ km and $\theta=60^{\circ}$, and since it is south (in the negative y - direction), the formula becomes $y=-d\sin\theta$.

Step2: Substitute values

Substitute $d = 5.0$ km and $\theta = 60^{\circ}$ into the formula. We know that $\sin60^{\circ}=\frac{\sqrt{3}}{2}\approx0.866$. So, $y=-5.0\times\sin60^{\circ}=-5.0\times0.866=- 4.33$ km.

Step3: Round the result

Rounding $-4.33$ km to the nearest tenth of a kilometer gives $-4.3$ km.

Answer:

-4.3 km