Mathematics: Atruck 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)?

Step 2Step-by-step explanation:9 was added on both sides...

Atruck driver travels at 59 miles per hour. the truck

ronaldhernandez598

16.01.2022

$661.4\ rpm$

Step-by-step explanation:

we know that

1 mile=63,360 inches

step 1

Find the circumference of the wheels

$C=2\pi r$

we have

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

substitute

$C=2\pi(15)$

$C=30\pi\ in$

assume

$\pi =3.14$

$C=30(3.14)=94.2\ in$

Remember that

The circumference of the wheels represent one revolution

Convert 59 miles per hour to inches per minute

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

using proportion find the number of revolutions

$\frac{1}{94.2}\frac{rev}{in}=\frac{x}{62,304}\frac{rev}{in}\\ \\x=62,304/94.2\\ \\x=661.4\ rev$

therefore

substitute

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

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