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A lamppost is 8 mt high. A man 2 mt tall walks away from the lamppost at a speed of 3 m/s. What is the rate of change in the length of the man's shadow when he is 10 mt from the lamppost?


Let LP be the lamppost, MA the man and AQ the shadow at time 't'
let
AQ =  x
 PA= y
using similar triangles

(2/8) = x / (x + y)

or

y = 3x

x = y / 3

{ given (dy/dt) =  3 m/s   (remember to see if all measurements are in the same unit ! ) }
now
x = y / 3

implies
(dx/dt)  = (1 / 3) (dy/dt)  = (1 / 3) (3) = 1 m/s

therefore length of the man's shadow is increasing at the rate of 1m/s when he is 10 mt from the lamppost.





 



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