25. jenny drives 10 miles south and 4 miles west to get to work. what is her displacement? round to the…

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