Question

1. jenny drives 10 miles south and 4 miles west to get to work. what is her displacement? round to the nearest hundredth. o 10.77 miles southwest o 12 miles southwest o 10 miles south o 14 miles southwest

Explanation:

Step1: Analyze the south - ward and west - ward displacements

Janny drives 10 miles south and 4 miles west. Displacement is a vector quantity. We can use the Pythagorean theorem to find the magnitude of the displacement vector. The Pythagorean theorem for a right - triangle with sides \(a\) and \(b\) and hypotenuse \(c\) is \(c=\sqrt{a^{2}+b^{2}}\), where \(a = 10\) (south - ward displacement) and \(b = 4\) (west - ward displacement).

Step2: Calculate the displacement

\[

$$\begin{align*} d&=\sqrt{10^{2}+4^{2}}\\ &=\sqrt{100 + 16}\\ &=\sqrt{116}\\ &\approx10.77 \end{align*}$$

\]
The direction is southwest.

Answer:

10.77 miles southwest