Question

I NEED HELP PLEASE, THANKS! :) A truck driver travels at 59 miles per hour. The truck tires have a diameter of 30 inches. What is the angular velocity of the wheels in revolutions per minute (rpm)? Show work.

Answer 1

Answer:

661.4 rpm

Step-by-step explanation:

we know that

1 mile=63,360 inches

step 1

Find the circumference of the wheels

C=2\pi rC=2πr

we have

r=30/2=15\ inr=30/2=15 in -----> the radius is half the diameter

substitute

C=2\pi(15)C=2π(15)

C=30\pi\ inC=30π in

assume

\pi =3.14π=3.14

C=30(3.14)=94.2\ inC=30(3.14)=94.2 in

Remember that    

The circumference of the wheels represent one revolution

Convert 59 miles per hour to inches per minute

59\ mi/h=59*63,360/60=62,304\ in/min59 mi/h=59∗63,360/60=62,304 in/min

using proportion find the number of revolutions  

\begin{lgathered}\frac{1}{94.2}\frac{rev}{in}=\frac{x}{62,304}\frac{rev}{in}\\ \\x=62,304/94.2\\ \\x=661.4\ rev\end{lgathered}94.21inrev=62,304xinrevx=62,304/94.2x=661.4 rev

therefore

substitute

62,304\ in/min=661.4\ rev/min=661.4\ rpm62,304 in/min=661.4 rev/min=661.4 rpm

Answer 2

Answer:  661 rpm

Step-by-step explanation:

Use the following conversions:

1 revolution = Circumference = 30 π inches

1 mile = 5280 feet

1 foot = 12 inches

1 hour = 60 minutes

$\dfrac{59\ mile}{1\ hour}\times \dfrac{1\ revolution}{30\pi \ inches}\times \dfrac{5280\ ft}{1\ mile}\times \dfrac{12\ in}{1\ ft}\times \dfrac{1\ hour}{60\ minutes}\\\\\\=\dfrac{62,304\ revolutions}{30\pi \ min}\\\\\\=\large\boxed{661.0\ revolutions\ per\ minute}$