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Chapter 10: Q. 71 (page 644)

Solar Heat - A mirror is shaped like a paraboloid of

revolution and is used to concentrate the rays of the sun at

its focus, creating a heat source. See the figure. If the mirror

is 20 feet across at its opening and is 6 feet deep, where will

the heat source be concentrated?

Short Answer

Expert verified

The heat source will be concentrated at 4.17 ft .

Step by step solution

01

Step 1.  Given information .

Consider the given distance and depth .

02

Step 2. Standard form of parabola used .

The standard form of parabola is x2=4aythe vertex of the parabola is at origin and focus is on the y positive axis .

03

Step 3. Find the distance .

To find the distance of heat source substitute the values x=202=10,y=6in the standard form of parabola .

x2=4ay102=4a路6a=4路17ft

Therefore the heat source will be concentrated at4路17ft

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