Speedometer+mix-up

=Ford F150 Tires = By: Dustin Mcvey, Gabby Lewis, David Jr., Kyle Borror

Two vehicles that are similar in all respects except thee 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?**
 * Problem #10- Checking the Speedometer**





** This is the WRONG way of doing it: **
Original tires: 35 inches in diameter. Substitution Tires: 24.4 inches in diameter & 29.2 inches in diameter

24.4 inch tires: 35x in. = 75mph X 24.4 in. 35x in. = 1,830 x = 52.285 mph 24.4 inch tires would make a truck travel at 52.285 mph while the onboard computer reads 75 mph. The Ford F150 Truck would travel at a slower speed when the wheels’ diameter has decreased.

29.2 inch tires: 35x in. = 29.2 in. X 75 mph 35x in. = 2,190 x = 62.57 mph 29.2 inch tires would make a truck travel at 62.57 mph while the onboard computer reads 75 mph. The Ford F150 Truck would travel faster with tires of 29.2 inch diameter than 24.4 inch diameter tires, but it would still be slower than the original 35 inch diameter tires.

This is the second WRONG way of doing it:
v=rw v= linear speed r=radius w=angular speed (radians/time) 75 mph 63,360 inches in a mile 79,200inches/min circumference=pi//xd// //C=76.65 inches//

24.4 inch tires: V=? R=24.4/2=12.2 inches W= 79,200/76.65= 1,033.268rad per min V=12.2(1,033.268) V= 12,605.8696 inches per min 756,352.176 inches/hour 11.937 mph 29.2 inch tires:

29.2 inch tires: V=11.936 R=14.6 inches W=1,028/min

=This is the right way of doing it:=

35 inch tires is the standard
V=75mph=4,752,000 inches/hour R=17.5 in W=?

4752000=17.5w W=271,542.857

24.4 inch tires:
V=? R=12.2 W=271,542.857 V=12.2(271,542.857) V=3,312,822.857 inches/hour

29.2 inch tires
V=? R=14.6 W=271,542.857 V=14.6(271,542.857) V=3,964,525.712 inches/hour