Wheel + Tire Trig Question

[Jru]

I've been stuck on this problem for a while and can't seem to get the correct answer for either of these, I've basically been adding the diameter of the inner wheel and adding the tire portion then trying to convert the measurement from mph to inches per hour to get the correct rotation measurement.

Your car's speedometer is geared to accurately give your speed using a certain tire size: 14.5" diameter wheels (the metal part) and 4.75" 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 traveling at 35 mi/hr?


rotations = ___ (Report answer accurate to 3 decimal places.)


(b) You buy new 5.5" tires and drive at a constant speed of 50 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.


Thanks the help guys.

 

[Deleted member 4993]

I've been stuck on this problem for a while and can't seem to get the correct answer for either of these, I've basically been adding the diameter of the inner wheel and adding the tire portion then trying to convert the measurement from mph to inches per hour to get the correct rotation measurement.

Your car's speedometer is geared to accurately give your speed using a certain tire size: 14.5" diameter wheels (the metal part) and 4.75" 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 traveling at 35 mi/hr?


rotations = ___ (Report answer accurate to 3 decimal places.)


(b) You buy new 5.5" tires and drive at a constant speed of 50 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.


Thanks the help guys.

Please show us exactly what did you calculate with numbers.

 

[Jru]

Thanks for the quick response, here's the work so far:

 

[Deleted member 4993]

I've been stuck on this problem for a while and can't seem to get the correct answer for either of these, I've basically been adding the diameter of the inner wheel and adding the tire portion then trying to convert the measurement from mph to inches per hour to get the correct rotation measurement.

Your car's speedometer is geared to accurately give your speed using a certain tire size: 14.5" diameter wheels (the metal part) and 4.75" 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 traveling at 35 mi/hr?


rotations = ___ (Report answer accurate to 3 decimal places.)


(b) You buy new 5.5" tires and drive at a constant speed of 50 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.


Thanks the help guys.

14.5/2 =7.25

7.25 + 4.75 = 12"

Now continue.......

 

[Steven G]

Thanks for the quick response, here's the work so far:

I think that you have the wrong value for r. Simple mistake.