Chapter 11.5, Problem 21WE

(a)

To determine

To Find: How far will the bike rider travel during the $5\min$ ride if the wheel are turning at a speed of $3revolutionper\sec$ ?

Answer to Problem 21WE

  $198,000cm$

Explanation of Solution

Given: Diameter is $70cm$ , use $\pi =\frac{22}{7}$

Given: $diameter=70$

  $\begin{array}{l}r=\frac{d}{2}\\ r=\frac{70}{2}\\ r=35\end{array}$

Circumference of a circle

  $\begin{array}{l}C=2\pi r\\ C=2\left(\frac{22}{7}\right)\left(35\right)\\ C=220\end{array}$

Wheel are turning at a speed of $3revolutionper\sec$

i.e.

  $220\times 3\times 60=39,600$

Now

Distance travelled in $5$ minutes.

  $39600\times 5=198,000cm$

Hence, $198,000cm$ .

(b)

To determine

To Find: How many revolution does the wheel make in $22km$ race?

Answer to Problem 21WE

  $10000$

Explanation of Solution

Given: Diameter is $70cm$ , use $\pi =\frac{22}{7}$

Distance travelled in $5$ minutes.

  $39600\times 5=198,000cm$

Now

  $\begin{array}{l}1km=100000cm\\ d=\frac{198000}{100000}\\ d=1.98km\end{array}$

Let $n$ be the number of revolutions.

Then revolution in $22km$ is

  $\begin{array}{l}22km=2,200,000cm\\ n=\frac{2,200,000}{220}\\ n=10000\end{array}$

Hence, $10000$ revolutions.