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# Related Rates watch

1. I have 2 questions that I am having issues with.

1- A 1.8m tall man walks away from a lightpost at a rate of 1.5m/s. The length of his shadow increases at a rate of 0.9m/s. How tall is the lightpost?

2- A lighthouse stationed at point P is x distance away from pointQ, the closest point on the shoreline. It's light rotates at 3rpm. It is found that the beam of light is moving across the shoreline at a rate of 200pi m/s when it passes over point R, which lies 1km from point Q. What is distance x (the distance from the lighthouse to the shoreline?)

If you could help me figure out the steps to either problem, that would be greatly appriciated.
2. Question 1 (hints)

Draw a diagram of the situation. you should have 2 similar right angled triangles.
let the height of the lightpost be h.
let the distance of the man from the post be x and the distance from the man to the tip of his shadow be y.
let the distance of the light post to the tip of the shadow be L. hence L=x+y .... (i)
use similar triangles to establish h/(x+y)=1.8/y ... (ii)

firstly solve (ii) for x and sub. into the expression for L (i). Differentiate wrt time. i.e. DL/Dt = .....

now solve (i) for y and sub. into the expression for L (ii) . again Differentiate wrt time .. i.e. DL/Dt=.....

these last 2 steps can be equated and you will find h.

if you are unsure at any stage then do ask.
d.

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Updated: October 18, 2015
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