SOLUTION: A car is moving at a rate of 79 miles per hour, and the diameter of its wheels is 1.8 feet. (Round your answers to three decimal places.) (a) Find the number of revolutions pe

Algebra.Com
Question 1203146: A car is moving at a rate of 79 miles per hour, and the diameter of its wheels is 1.8 feet. (Round your answers to three decimal places.)

(a) Find the number of revolutions per minute the wheels are rotating.
revolutions per minute

(b) Find the angular speed of the wheels in radians per minute.
radians per minute
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
A car is moving at a rate of 79 miles per hour, and the diameter of its wheels is 1.8 feet.
(Round your answers to three decimal places.)
(a) Find the number of revolutions per minute the wheels are rotating.
revolutions per minute
(b) Find the angular speed of the wheels in radians per minute.
radians per minute
~~~~~~~~~~~~~~~~~~~~~~~~~ 

(a)  is solved in three steps.

     First step is to convert 79 miles per hour to feet per minute

           79 miles per hour =  feet per minute.


     Second step is to write the circumference of the weel

           circumference =  =  3.14159*1.8 feet.


     After that, the number of revolutions per minute is

           the number of revolutions per minute =  = 1229.358  (rounded).  ANSWER



(b)  1229.358 revolutions per minute is   = 2*3.14159*1229.358 = 7724.278 radians per minute  (rounded).  ANSWER

Solved.

--------------------

Three decimal is exceeding precision for such calculations.
Your input data is correct to one decimal place - so the result should be with one decimal place, not more.

Otherwise, calculations are not consistent with common sense.



Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Answers:
  1. 1229.384 revolutions per minute (rpm)
  2. 7724.444 radians per minute
Each result is approximate.

==============================================================================

Work Shown for part (a)

1 mile = 5280 ft
1 hour = 60 min

circumference = pi*diameter
C = pi*d
C = pi*1.8
C = 1.8pi
1 revolution = 1.8pi feet



"miles" units cancel

"hours" units cancel

"feet" units cancel



After those cancellations, the only thing left will be "rev" up top and "min" down below
That gives the angular speed unit "revolutions per minute". This abbreviates to RPM.

The next step is to use a calculator, or scratch paper, to compute the following






This value is approximate. I used my calculator's stored version of pi to get the most accuracy possible.

After rounding to 3 decimal places.
This equation is valid only when the wheel diameter is 1.8 feet.

The approximate result is roughly 1229.384 rpm.

----------------------------------

Work Shown for part (b)

Refer to the previous part when we got to the step
I'll use that to avoid decimal rounding error.



"Rev" units cancel

The pi's cancel







This is approximate. The 4's go on forever.

After rounding to 3 decimal places.


Summary
79 mph = 1229.384 rpm
79 mph = 7724.444 radians per minute
Each decimal value is approximate.
This applies only when the wheel diameter is 1.8 feet.
RELATED QUESTIONS

I have a test tomorrow and for some reason i just can't understand these problems!!... (answered by jim_thompson5910,Alan3354,LinnW)
please answer this question: a truck is moving at a rate of 105 kilometers per hour, and (answered by TimothyLamb,stanbon,josgarithmetic)
a truck is moving at a rate of 90 kilometers per hour, and the diameter of its wheels is... (answered by ankor@dixie-net.com)
A car is traveling at a rate of 54 miles per hour. What is the car's rate in feet per... (answered by Alan3354)
A car is traveling at a rate of 90 miles per hour. What is the car's rate in feet per (answered by t0hierry)
A car is traveling at a rate of 44 feet per second. What is the car's rate in miles per... (answered by ikleyn,josgarithmetic)
A car is traveling at a rate of miles 66 per hour. What is the car's rate in miles per... (answered by Theo)
A car is traveling at a rate of 93 miles per hour. What is the car's rate in miles per... (answered by josmiceli)
A car is traveling at a 50 km rate of kilometers per hour. What is the car's rate in... (answered by math-vortex)