A car is traveling at 34 miles per hour. If its tires have a diameter of 14 inches, how fast are the car’s tires turning? Express the answer in revolutions per minute and round to two decimal
places.
To determine how fast the car's tires are turning, we need to calculate the number of revolutions per minute.
First, we need to convert the car's speed from miles per hour to inches per minute. Since there are 5280 feet in a mile, and 12 inches in a foot, we can calculate the car's speed in inches per minute as follows:
Speed (in inches per minute) = Speed (in miles per hour) * 5280 (feet/mile) * 12 (inches/foot) / 60 (minutes/hour)
Substituting the given speed of 34 miles per hour into the equation:
Speed (in inches per minute) = 34 * 5280 * 12 / 60 = 272640 inches per minute
Next, we need to calculate the circumference of the car's tire, which is equal to the distance traveled in one revolution. The formula for calculating the circumference is:
Circumference (in inches) = π * Diameter (in inches)
Substituting the given diameter of 14 inches into the equation:
Circumference (in inches) = 3.14159 * 14 = 43.98204 inches
Now, we can calculate the number of revolutions per minute by dividing the speed (in inches per minute) by the circumference (in inches):
Revolutions per minute = Speed (in inches per minute) / Circumference (in inches)
Substituting the previously calculated values into the equation:
Revolutions per minute = 272640 / 43.98204 = 6199.12
Rounding the answer to two decimal places, the car's tires are turning at approximately 6199.12 revolutions per minute.