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Expert: Sherry Wallin - 11/6/2010


Question
A car's rear windshield wiper rotates 130°. The total length of the wiper mechanism is 25 inches and wipes the windshield over a distance of 14 inches. Find the area covered by the wiper. (Round your answer to one decimal place.)

Also can you please tell me how to do this problem as well?

A wheel of radius 14 in. is rotating at a rate of 2700 rpm. (Enter your answers in terms of π.)
(a) Find the angular speed (in radians per minute).
(b) Find the linear speed of a point on the circumference (in ft/min).

Thanks!

Answer

windshield wiper probl
Kristin~ Here is a revised answer


Here is the answer to your questions with a drawing labeled and attached and below is the written only solutions:

You have an arc with a radius of 11” and an arc with a radius of 25” because you want the 14” sweep so 25” – 14” = 11”. And thus you will want to find the area of the sector covered between the two arcs. You will need the formula for the area of a sector of a circle which is  (1/2)r^2*theta. Note you need theta to be in radians so first let’s change 130° to radians:

theta = (pi/180)130 = (13/18)pi radians

Now the area of the 130° sector is (1/2)(25^2)(13/18)*pi = 225.69pi  and then we will need to subtract off the area of the sector with radius of 11”: (1/2)(11^2)(13/18)*pi = 43.69pi =>
and the difference is (225.69 - 43.69)pi = 182pi in^2 which is the area swept out by the 14 inch windshield wiper blade over the 130 deg sweep.


The angular speed omega is defined to be the angle theta measured in radians that is swept out divided by the elapsed time
omega = (2700 rev/min)*(2pi rad/rev)= 5400pi rad/min

Then the linear speed is defined to be  v = r*omega so the linear speed is (5400 pi rad/min)(1 ft/12 in)(14 in) = 6300 pi  ft/min

Math Prof

Sherry Wallin

Expertise

I can answer most questions up through Calculus and some in Number Theory and Abstract Algebra.

Experience

I have had my Bachelor's Degree since 1987 and have been a teacher since 1988. I earned my Masters Degree in Mathematics May 2010. I have been teaching at the same community college since 2002.

Education/Credentials
I have taught 12 years at the community college level, medical college, and technical college as well as a high school instructor and alternative education instructor and charter school instructor.

Awards and Honors
Master's GPA 3.56 Bachelor's GPA 3.34 Post grad work not degree related GPA 4.0

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