SOLUTION: Your car’s speedometer is geared to accurately give your speed using a certain tire size: 15” diameter wheels (the metal part) and 4.35” tires (the rubber part). (a) If

Algebra ->  Angles -> SOLUTION: Your car’s speedometer is geared to accurately give your speed using a certain tire size: 15” diameter wheels (the metal part) and 4.35” tires (the rubber part). (a) If       Log On


   

Question 1159190: Your car’s speedometer is geared to accurately give your speed using a certain tire size: 15” diameter wheels (the metal part) and 4.35” tires (the rubber part).
(a) If your car's instruments are properly calibrated, how many times should your tire rotate per second if you are travelling at 55 mi/hr?
rotations =
Report answer accurate to 3 decimal places.
(b) You buy new 5.25” tires and drive at a constant speed of 60 mph (according to your car’s instrument). However, a cop stops you and claims that you were speeding. How fast did the radar gun clock you moving?
actual speed =
mph
Report answer accurate to the nearest whole number.
(c) Then you replace your tires with 3.6” tires. When your speedometer reads 25 mph, how fast are you really moving?
actual speed =
mph
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Your car’s speedometer is geared to accurately give your speed using a certain tire size: 15” diameter wheels (the metal part) and 4.35” tires (the rubber part).
(a) If your car's instruments are properly calibrated, how many times should your tire rotate per second if you are travelling at 55 mi/hr?
The total diameter of he tire: 15 + 4.35 + 4.35 = 23.7 inches
The circumference: pi%2A23.7+=+74.4557 inches
Find the no. of inches traveled in 1 sec at 55 mph
%28%2855%2A5280%2A12%29%29%2F%28%2860%2A60%29%29 = 968 inches
Find the rev/sec of the tire
968%2F74.4557 = 13.001 rotations/sec
:
(b) You buy new 5.25” tires and drive at a constant speed of 60 mph (according to your car’s instrument).
However, a cop stops you and claims that you were speeding.
How fast did the radar gun clock you moving?
The speedometer still thinks you have the original tires
Find the the rev/sec at 60 mph
%28%2860%2A5280%2A12%29%29%2F%28%2860%2A60%29%29 = 1056 inches
Find the rev/sec of the tire
1056%2F74.4557 = 14.1829 rotations/sec
Find the diameter of the new tire: 15 + 5.25 + 5.25 = 25.5 inches
Find the new circumference: pi%2A25.5 = 80.1106 inches
Find how far you travel in 1 hr at this rotation and new circumference in mph
%28%283600%2A80.1106%2A14.1829%29%29%2F%28%2812%2A5280%29%29 = 64.557 ~ 65 mph, actual speed
:
(c) Then you replace your tires with 3.6” tires. When your speedometer reads 25 mph, how fast are you really moving?
The speedometer still thinks you have the original tires
Find the the rev/sec at 25 mph
%28%2825%2A5280%2A12%29%29%2F%28%2860%2A60%29%29 = 440 inches
Find the rev/sec of the tire
440%2F74.4557 = 5.9096 rotations/sec
Find the new diameter: 15 + 3.6 + 3.6 = 22.2 inches
Find the new circumference: pi%2A22.2 = 69.743 inches
Find how far you travel in 1 hr at this rotation and new circumference in mph
%28%283600%2A69.743%2A5.9096%29%29%2F%28%2812%2A5280%29%29 = 23.4178 ~ 23 mph actual speed
:
A lot of tedious math here, better check my calculations.CK