Maths question, Differential equations.... Help? REALLY appreciated!
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Maths question, Differential equations.... Help? REALLY appreciated!

[From: ] [author: ] [Date: 12-11-20] [Hit: ]
photobucket.You could of course let the boy begin walking at the pole but it works as well if we let him begin walking at 18 feet.......
I can normally do these really well. But in this case I have barely any idea where to start... Anyone fancy helping me out? :) Show me how you did it, as well.

A light is at the top of a 16ft pole. A boy 5ft tall walks away from the pole at a rate of 4ft/second. At what rate is the distance from the base of the pole to the tip of his shadow increasing when he is 18ft from the pole? And At what rate is the length of his shadow then increasing?

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I did a little picture for you.
http://s1357.beta.photobucket.com/user/J…

x is the distance between the boy and the pole
s is the length of the shadow
t = s+x
with some trigonometry you find out that
s= 5 * x/16

for the first question you need to find a function that gives you the distance t depending from time (h)

You could of course let the boy begin walking at the pole but it works as well if we let him begin walking at 18 feet.

f(h)= length of shadow after h seconds + distance from pole = 5* (4*h +18)/16 + 4h+18
=(4h+18)*(1+ 5/16)

f ' (0)= derivation of f at h=0 = 4* (1+ 5/16)= 21/4 ft/sec

g(h)= length of shadow after h seconds = 5* (4*h +18)/16

g ' (0)= derivation of g at h=0 = 5/4 ft/sec
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