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 find the speed at which the car's tires are turning, we need to convert the car's speed from miles per hour to inches per minute.
1. Convert 34 miles per hour to inches per minute:
34 miles = 34 * 5280 feet (1 mile = 5280 feet)
= 179,520 feet
179,520 feet = 179,520 * 12 inches (1 foot = 12 inches)
= 2,154,240 inches
Therefore, the car is traveling at a speed of 2,154,240 inches per hour.
2. Now, to find the speed in inches per minute, divide by 60 (since there are 60 minutes in an hour):
2,154,240 inches / 60 minutes = 35,904 inches per minute
Now, we need to find the number of revolutions per minute.
3. To find the circumference of the tire, we use the formula C = πd, where C represents the circumference and d is the diameter. So, for the given tire with a diameter of 14 inches, the circumference would be:
Circumference = π * 14
= 43.9823 inches (rounded to four decimal places)
4. Finally, to find the number of revolutions per minute, divide the speed in inches per minute by the circumference of the tire:
35,904 inches per minute / 43.9823 inches per revolution
≈ 815.22 revolutions per minute (rounded to two decimal places)
Therefore, the car's tires are turning at a speed of approximately 815.22 revolutions per minute.
To find out how fast the car's tires are turning, we need to convert the car's speed from miles per hour to inches per minute. Then we can use the tire's diameter to calculate the number of tire revolutions per minute.
First, let's convert the car's speed from miles per hour to inches per minute. We know that there are 5,280 feet in a mile and 12 inches in a foot, so there are 5,280 * 12 = 63,360 inches in a mile.
To convert miles per hour to inches per minute, we multiply the speed by the conversion factor:
34 miles/hour * 63,360 inches/mile = 2,154,240 inches/ hour.
To convert from inches per hour to inches per minute, we divide by 60:
2,154,240 inches/hour / 60 = 35,904 inches/minute.
Now, let's calculate the number of tire revolutions per minute. The formula to calculate the number of revolutions per minute (RPM) is:
RPM = Inches per minute / Circumference of tire.
The circumference of a circle is calculated by multiplying its diameter by pi (approximately 3.14159):
Circumference = Diameter * pi.
Given that the tire diameter is 14 inches, the circumference of the tire is:
14 inches * 3.14159 = 43.98204 inches.
Now we can calculate the number of tire revolutions per minute:
RPM = 35,904 inches/minute / 43.98204 inches = 815.59 revolutions/minute.
Rounding to two decimal places, the car's tires are turning at approximately 815.59 revolutions per minute.