Related Rates: Man and Spotlight

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Homework Help Overview

The problem involves related rates in the context of a person walking towards a wall while casting a shadow, with a spotlight illuminating the scene. The specific question is about the rate at which the length of the shadow on the wall is decreasing as the person approaches the wall.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the setup of the problem, including the use of similar triangles to relate the distances and heights involved. There are questions about how to establish the necessary equations for solving the problem.

Discussion Status

The discussion has progressed with participants offering suggestions to visualize the problem and relate the dimensions through similar triangles. Some participants express difficulty in setting up the equations, while others provide guidance on how to approach the problem.

Contextual Notes

There is mention of needing to draw a picture to aid understanding, and participants are exploring how to translate the given information into a mathematical framework. The original poster indicates a struggle with the initial setup rather than the solving process itself.

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Homework Statement


A 2m tall person walks toward toward a wall at 1.6 m/s. A spotlight 12 m away from the wall shines at it. How fast is the length of his shadow on the wall decreasing when he is 4m away from the wall?

I tried a few different things with trig, none of which worked.
 
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like what?
 
Well, actually I couldn't figure out how to setup the equation to begin with.
 
ok so start by drawing a picture, and try and relate the distnace of the man from the light or wall to the height of the shadow - think similar triangles
 
Yeah, that's where I run into problems.
 
ok so what do you need a hand with?
 
How can I go about setting up the problem? How can I go about finding an equation to solve? I understand how to solve these problems, but not how to go about setting up their equations.
 
Think about the spot light creating a triangle and then insert the man to create a second smaller triangle. Using the numbers you have in the question, you can get your equation from that by setting the two similar triangles equal to each other - I can't remember the exact name for that, sorry. Ex. base/height of triangle one = base/height of triangle two then cross multiply and solve for your unknown that may or may not start with an s.
 
I managed to get it. Sorry it took so long to get back. Thanks for your help!
 

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