The speedometer of John's truck uses the revolutions of his tires to calculate the speed of the truck.
How many revolutions per minute do the tires make when the truck is traveling at 55 miles per hour?
(picture with tires with diameter of 26 in.)
Suppose John buys tires with a diametr of 30 inches. When the speedometer reads 55 miles per hour, the tires would still revolve at the same rate as before. However, with the new tires, the truck travels a different distance in each revolution. Calculate the actual speed when the speedometer reads 55 miles per hour.
Thank you so much.
Circumference = π diameter = 3.14 * 26
55 mph = 4,840 feet/hr = 4,840 * 12 inches/hour = 4,840*12inches/60 minutes
Divide the above answer by circumference to get revolutions/minute
Use the above process to get the answer to your second question.
711.4
POGGERS
To find the number of revolutions per minute (RPM) the tires make when the truck is traveling at 55 miles per hour, we need to consider the relationship between speed, distance, and time.
First, let's calculate the circumference of the tires using the given diameter of 26 inches. The circumference (C) of a circle can be calculated using the formula:
C = π * D,
where D is the diameter. Substituting the given diameter of 26 inches, we have:
C = π * 26 inches.
Next, we need to convert the speed of the truck from miles per hour to inches per minute. We know that there are 5,280 feet in a mile, 12 inches in a foot, and 60 minutes in an hour. So, multiplying 55 miles per hour by these conversion factors:
Speed = 55 mi/hr * (5280 ft/mi) * (12 in/ft) * (1 hr/60 min).
Now, we have the speed in inches per minute. To find the number of revolutions per minute, we divide the speed by the circumference of the tires:
RPM = Speed / C.
However, before calculating the RPM, we need to convert the speed to miles per hour using the new tire diameter of 30 inches. We can use the concept of proportions to find the actual speed when the speedometer reads 55 miles per hour.
The proportion relating the speeds with different tire diameters is:
(Original Speed) / (Original Tire Diameter) = (Actual Speed) / (New Tire Diameter).
Plugging in the values we know:
55 / 26 = Actual Speed / 30.
Now we can solve for the actual speed:
Actual Speed = (55 / 26) * 30.
Finally, we can calculate the RPM for the new tire diameter using this actual speed and the formula RPM = Speed / C.
Let me perform the calculations for you.