related rates problem: A street light is mounted at the top of a 15ft pole. A 6ft tall man walks away from the pole at 5ft/second along a straight path. How fast is the top of his shadow moving when he is 40ft away from the pole?

Question

related rates problem:  A street light is mounted at the top of a 15ft pole. A 6ft tall man walks away from the pole at 5ft/second along a straight path. How fast is the top of his shadow moving when he is 40ft away from the pole?

amistre64 · Answer

might need a right triangle for this

anonymous · Answer

yup i have an answer but Im not sure if i achieved it the correct way

amistre64 · Answer

|dw:1329434220776:dw|

amistre64 · Answer

we have similar triangles: such that:

$$\frac{15}{w+s}=\frac{6}{s}$$

amistre64 · Answer

we know the rate of w with repect to time; w' = 5

amistre64 · Answer

s' = w' + s' in this case I beleive

amistre64 · Answer

15s = 6w+6s

15s-6s = 6w


s(15-6) = 6w

s = 6w/9 = 2w/3

ds/dw = 2w'/3

amistre64 · Answer

w' = 5, s' = 10/3 if i did it right

so w'+s' =  25/3

any idea if thats good?

anonymous · Answer

thats what i got haha. I'm studying your explanation more thoroughly...

amistre64 · Answer

im always ;eary of this one casue the 40 feet seems to be superfluous to the overall mathing

amistre64 · Answer

leary even lol

amistre64 · Answer

example 6 http://tutorial.math.lamar.edu/Classes/CalcI/RelatedRates.aspx

anonymous · Answer

many thanks that is just what i needed