Original Size
Posted February 12, 2008
By admin
How long does it take for the area A to increase to 5 times its original size?
A satellite camera takes a rectangular-shaped picture. The smallest region that can be photographed is a 5 km by 7 km rectangle. As the camera zooms out, the length "L" and the width of "W" of the rectangle increase at a rate of 2 km/sec. How long does it take for the area "A" to increase to 5 times its original size?
The smallest region that can be photographed is
5*7 = 35 square km
so we want to know how long it takes to zoom out to an area of
35 * 5 = 175 square km.
Notice that the length and width increase at the same rate, 2 km/sec, and they start out with a difference of two, so when the width has increased from 5 to x, the length will have increased from 7 to x+2. At the desired coverage area, then,
x(x+2) = 175
x^2 + 2x = 175
x^2 + 2x + 1 = 176 [completing the square]
(x+1)^2 = 176
x+1 = ±4√11
x = -1 ±4√11
Since a negative value for x is meaningless here, x must be
-1 + 4√11 = about 12.27 km
and the time it took to increast to that value was
(12.27 - 5) km / (2 km/sec) = about 3.63 seconds
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