Chapter 8.7, Problem 47STP

(a)

To determine

To calculate:

The vectors representing both paths

Answer to Problem 47STP

The vectors representing both paths is $\langle 7,2\rangle$

Explanation of Solution

Given information:

  $\begin{array}{l}\langle u_1,u_2\rangle =\langle 2,3\rangle \\ \langle v_1,v_2\rangle =\langle 5,-1\rangle \end{array}$

Formula used:

The resultant vector of the two path vectors is given by the following expression:

  $\langle u_1,u_2\rangle +\langle v_1,v_2\rangle =\langle u_1+v_1,u_2+v_2\rangle$

Calculation:

The vectors representing both paths are the resultant vector of the two path vectors as:

  $\begin{array}{l}R=\langle 2+5,3-1\rangle \\ R=\langle 7,2\rangle \end{array}$

(b)

To determine

To calculate:

The distance between girl and her car

Answer to Problem 47STP

The distance between girl and her car is $7.3mi$

Explanation of Solution

Given information:

From sub-part (a):

The vectors representing both paths is $\langle x_1,y_1\rangle =\langle 7,2\rangle$

Formula used:

The distance formula of the two vectors is given by the following expression:

  $\left|\overline{R}\right|=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-x_1\right)}^2}$

Calculation:

The distance between girl and her car is calculated as:

  $\begin{array}{l}\left|\overline{R}\right|=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-x_1\right)}^2}\\ \left|\overline{R}\right|=\sqrt{{\left(7-0\right)}^2+{\left(2-0\right)}^2}\\ \left|\overline{R}\right|=\sqrt{49+4}\\ \left|\overline{R}\right|=\sqrt{53}\\ \left|\overline{R}\right|=7.3mi\end{array}$