Posted by A on Sunday, November 13, 2011 at 12:42pm.
A light is on the ground 20m from a barn. A 2m tall llama walks from the light directly toward the side of the barn at 1m/s. How fast is the height of the llama's shadow on the barn changing when he's 14m from the barn? (draw and label a nice diagram first!)

College Calculus  Steve, Monday, November 14, 2011 at 12:28am
If x is the diatsnace from the light to the llama, and h is the height of the shadow on the wall, then using similar triangles,
h/20 = 2/x
hx = 40
At 14m from the barn, x=6 and h = 40/6 = 20/3
hx' + xh' = 0
(20/3)(1) + 6h' = 0
h' = 10/9
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