How fast is the tire traveling in mph if it does 2 rotations in 2 seconds with a diameter of 27 inches for the tire?
if it does 2 rotations in 2 seconds, then it does
1 rotation in 1 second
or 2π(13.5) inches per second
= 2π(13.5)/12 ft /sec
=7.06858.... ft/s (I stored in in my calculator memory for accuracy)
= (7.06858...)/5280 miles / (1/3600) hr
= appr 4.82 mph
circumference of a circle:
C=2*pi*r
where r=radius=27/2=13.5ft
pi=3.14
C=84.78
It's making 2 rotations every 2 seconds or in other words, 1 rotation every 1 second.
note its asking for mph:
1hour=3600
12inch=1foot
1mile=5280
Formula to solve this:
(n*C*3600)/(12*5280)
where n= number of rotations per sec
C=circumferene, and everything else is conversions to get to mph
(1*84.78*3600)/(12*5280) = 4.816mph
Someone check the work and method just to be sure.
To determine the speed of the tire in miles per hour (mph), we need to determine the distance the tire covers in one hour.
First, we need to find the distance covered by the tire in one rotation. This can be determined using the formula for the circumference of a circle:
Circumference = π × Diameter
Given the diameter of the tire as 27 inches, we can calculate the circumference:
Circumference = π × 27 inches
Next, we need to calculate the distance covered by the tire in 2 seconds, which is equivalent to 2/60 minutes:
Distance covered in 2 seconds = Circumference × 2
To determine the distance in 1 minute, we can multiply the distance covered in 2 seconds by 30:
Distance covered in 1 minute = Distance covered in 2 seconds × 30
Finally, to calculate the distance in one hour, we multiply the distance covered in 1 minute by 60:
Distance covered in one hour = Distance covered in 1 minute × 60
Now, we can substitute the values and solve the equation:
Circumference = π × 27 inches
Distance covered in 2 seconds = (π × 27 inches) × 2
Distance covered in 1 minute = (π × 27 inches × 2) × 30
Distance covered in one hour = (π × 27 inches × 2) × 30 × 60
Finally, we can convert the distance from inches to miles:
Distance covered in one hour (in miles) = (Distance covered in one hour ÷ 1 mile)
This will give us the speed of the tire in miles per hour (mph).