Chapter 7, Problem 1WUE

Math Review A circular track has a radius of 125 m. (a) Calculate the distance around the track. (b) If a runner jogs 275 m along the track, through what angle has he run?

To determine

The distance around the track.

Answer to Problem 1WUE

Solution: The distance around the track is $785\text{m}$.

Explanation of Solution

Given info: The radius of the circular track is $125\text{m}$.

The formula for the distance around the track is,

$c=2\pi r$

• $r$ is radius of the track.

Substitute $125\text{m}$ for $r$ to find $c$.

$\begin{array}{c}c=2\left(3.14\right)\left(125\text{m}\right)\\ =785\text{m}\end{array}$

Conclusion:

Therefore, the distance around the track is $785\text{m}$.

To determine

The angle he has run.

Answer to Problem 1WUE

Solution: The angle he has run is $2.20\text{radians}$.

Explanation of Solution

Given info: The distance travelled by the runner is $275\text{m}$ and distance of the circular track is $785\text{m}$.

The formula for the angle he has run is,

$\theta =\left(2\pi \text{radian}\right)\left(c\text{'}/c\right)$

• $c\text{'}$ is the distance travelled by the runner.
• $c$ is distance of the circular track.

Substitute $275\text{m}$ for $c\text{'}$ and $785\text{m}$ for $c$ to find $\theta$.

$\begin{array}{c}\theta =\left(2\pi \text{radian}\right)\left(275\text{m}/785\text{m}\right)\\ =2.20\text{radians}\end{array}$

Conclusion:

Therefore, the angle he has run is $2.20\text{radians}$.