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August 30, 2014

August 30, 2014

Posted by **Stuck** on Sunday, June 20, 2010 at 10:35pm.

I can draw the diagram, and can organize all the information, but can't seem to bring it all together into an equation I can work with.

- Calculus -
**MathMate**, Sunday, June 20, 2010 at 10:56pmDistance between street lights, L = 40m

Distance of darkest point from left light = x

Distance of darkest point from right light (twice as strong) = L-x

Height of street light from ground in metres

= h

Assuming

1. The right light is twice as strong as the left, and

2. the "darkest" point is located along a straight line joining the two lights.

Illumination by left light, I1

= K/(h²+x²) K=light constant

Illumination by right light, I2

= 2K/(h²+(L-x)²)

Total illumination, I

= I1+I2

=K/(h²+x²)+2K/(h²+(L-x)²)

Differentiate with respect to x and equate to zero and solve for x (in terms of K and h) to find the minimum luminosity.

I get 17.7 m from the weaker light, assuming the height above ground h=0.

- Calculus -
**Stuck**, Sunday, June 20, 2010 at 11:01pmOh I see! Thank you!

- Calculus -
**saud**, Sunday, April 24, 2011 at 2:06pmA street light is at the top of a 19 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 5 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 40 ft from the base of the pole?

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