Trae E.

asked • 10/28/22

A patrol car is parked 45 feet from a long warehouse (see figure).


The revolving light on top of the car turns at a rate of 26 revolutions per minute. How fast is the light beam moving (in ft/sec) along the wall when the beam makes angle 𝜃 = 85° with the line perpendicular from the light to the wall? (Round your answers to two decimal places.)

(c) 𝜃 = 85° ? ft/sec



1 Expert Answer

By:

Kirsten E. answered • 10/29/22

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Doug C.

Thinking dtheta/dt should be in radians?
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10/29/22

Kirsten E.

tutor
I originally did it that way, but then observed that we are asked to find the result when theta = 85 degrees, so I started over.
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10/29/22

Doug C.

Actually the 85 degrees can still be used to find the sec(theta)^2, but the rate of change of theta should be in radians. 26 revs(2pi) gives a very different answer than 26revs(360 degrees). If you use degrees for the rate of change the units for the rate of change in y will be foot.degrees./min, but if you use radians it will be the correct feet/min. The sec^2(theta) will give the same value whether theta is in degrees or radians.
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10/29/22

Kirsten E.

tutor
Ah yes, this is true.
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10/29/22

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