Chapter 4.1, Problem 21P

Mitwaukee is 121 mi (air miles) due west of Grand Rapids. Maria drives 255 mi in 4.75 h from Grand Rapids to Mitwaukee around Lake Michigan. Find (a) her average driving speed and (b) her average travel velocity.

To determine

Find the average driving speed of the person.

Answer to Problem 21P

The average driving speed of the person is $\underset{\_}{53.7\frac{\text{mi}}{\text{h}}}$.

Explanation of Solution

Given data:

The distance travelled by the person $\left(s\right)$ is 255 mi.

The time taken by the person to travel the given distance $\left(t\right)$ is 4.75 h.

Formula used:

Write the expression to find the average velocity in terms of distance and duration as follows.

$v_{\text{avg}}=\frac{s}{t}$ (1)

Here,

$s$ is the distance travelled by the person, and

$t$ is the time taken by the person to travel the given distance.

Calculation of average driving speed of the person$\left(v_{\text{avg}}\right)$ in terms of $\frac{\text{mi}}{\text{h}}$:

Substitute 255 mi for $s$, and 4.75 h for $t$ in equation (1),

$\begin{array}{c}{v}_{\text{avg}}=\frac{255\text{mi}}{4.75\text{h}}\\ =53.6842\frac{\text{mi}}{\text{h}}\\ \simeq 53.7\frac{\text{mi}}{\text{h}}\end{array}$

Conclusion:

Thus, the average driving speed of the person is $\underset{\_}{53.7\frac{\text{mi}}{\text{h}}}$.

To determine

Find the average travel velocity of the person.

Answer to Problem 21P

The average travel velocity of the person is $\underset{\_}{25.5\frac{\text{mi}}{\text{h}}}$ in the direction of west.

Explanation of Solution

Given data:

The travel distance $\left(s\right)$ is 121 mi.

The time duration to travel the given distance $\left(t\right)$ is 4.75 h.

Calculation of average travelvelocity of the person $\left(v_{\text{avg}}\right)$:

Substitute 121 mi for $s$, and 4.75 h for $t$ in equation (1),

$\begin{array}{c}{v}_{\text{avg}}=\frac{121\text{mi}}{4.75\text{h}}\\ =25.4736\frac{\text{mi}}{\text{h}}\\ \simeq 25.5\frac{\text{mi}}{\text{h}}\end{array}$

As the given displacement is in the direction of west, the direction of obtained velocity is in the west direction.

Conclusion:

Thus, theaverage travel velocity of the person is $\underset{\_}{25.5\frac{\text{mi}}{\text{h}}}$ in the direction of west.