Checking+the+Speedometer!!!!!!

Problem Eleven: Two Vehicles that are similar in all respects except the size of the tire have different linear speeds. Assume that you have purchased a standard Ford F150 and have decided to replace the standard tires with either a tire with a diameter of 29.2 inches or a tire with a diameter of 24.4 inches without updating the onboard computer. How fast will the truck actually be traveling when the speedometer reads 75 mph for each new tire?

w= angular speed(Found on 1010tires.com)
=Standardized Tire:= 32.15 inches in diameter 16.07=radius (revs/mi)(speed)=rev/hr (646.9)(75)=48517.5rev/hr (2pi)(48517.5)= angular speed (2pi)(48517.5)(16.07)= V V= 4900374.423 in/hr 2pi is used because we need to get the angular speed in radians. Conversion from in/hr to mi/hr: 4900374.423/12/5280= 77.34 mi/hr

Actual speed of a standard tire (32.15 inches) is 77.34 miles per hour.
=29.2 inch tires:= 29.2 inches in diameter 14.6=radius (revs/mi)(speed)=rev/hr (707.4)(75)=53055 rev/hr (2pi)(53055)= angular speed (2pi)(53055)(14.6)= V V= 4866974.188 in/hr 2pi is used because we need to get the angular speed in radians. Conversion from in/hr to mi/hr: 4866974.188/12/5280= 76.81mi/hr

Actual speed of a 29.2 inch tire is 76.81 miles per hour.
=24.4 inch tires:= 24.4 inches in diameter 12.2=radius (revs/mi)(speed)=rev/hr (832.3)(75)= 6422.5 (2pi)(62422.5)= angular speed (2pi)(62422.5)(12.2)= V V= 4784988.045 in/hr 2pi is used because we need to get the angular speed in radians. Conversion from in/hr to mi/hr: 4784988.045/12/5280= 75.52 mi/hr

Actual speed of a 24.4 inch tire is 75.52 miles per hour.


=Connection to the Trigonometric Concepts:= To find the actual speed of a F150 truck we used the linear speed equation. In the linear speed equations, we needed to first find out the radius and angular speed. The diameter was already given to us, so we just divided the diameter by two to find the radius, which is half the diameter. The angular speed was a little more challenging to find, on the website 1010tires.com there was a conversion table. We took 75 miles per hour and multiplied it by the revolutions per mile, which the units cancel to become revolutions per hour. Then when we wanted to find the entire linear speed, we took the revolutions per hour multiplied it by 2 pie, and then the radius. We took it by 2 pie, because that was one revolution of the tire in radians. Then when we got the linear speed in inches per hour. We did the conversions of inches per hour to miles per hour by dividing by 12 and then 5280. Once we did all the above steps we got the actual speed a F150 truck was going with the standardized tire, 29.2 inch tire, and then the 24.4 inch tire, which was greater than 75 miles per hour.

RONALD PERRY JILLIAN EBERLY ZACH MARTIN