Shadow Height on Wall: 2.6m Light Source

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Homework Help Overview

The problem involves determining the height of a shadow cast on a wall by a rectangular piece of cardboard held in front of a point light source. The cardboard is 21.7 cm high, positioned 1.0 m from the light source, and 2.6 m away from the wall.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of similar triangles to relate the dimensions of the cardboard and the shadow on the wall. There is confusion about the correct ratios and the distances involved in the setup.

Discussion Status

Some participants have attempted calculations using ratios but have encountered errors. Others have suggested drawing the scenario to visualize the relationships between the dimensions. A participant claims to have found a correct answer but seeks further understanding of the reasoning behind it.

Contextual Notes

There is mention of a lack of instruction on this topic in class and uncertainty about the correct application of ratios in the context of similar triangles. Participants are exploring the implications of their calculations and the definitions involved.

dblader
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1. A rectangular piece of cardboard 21.7cm high is held 1.0m in front of a point source of light. The cardboard is 2.6m away from a wall. How tall is the shadow on the wall?

I have no idea how to do this my prof never talked about this in class and I looked threw the book with no help. I emailed my prof and he told me to google it. The way I thought to do it was to use the b/a=c/d=e/f , and use the ratio of 2.6m/1m = d/.217m and i got d=.56m but it wasn't correct. if any of you guys know how to do this I would greatly appreciate it.

Thanks,

Dblade
 
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Just make a drawing. Your light is a point source. Won't then the projected dimensions be able to be determined by like triangles?
 
what do you mean by like triangles.
 
dblader said:
what do you mean by like triangles.

Like triangles similar triangles, etc.

Won't the ratio of the sides be equal?
 
im pretty sure that they would be equal. a=distance from source to object b=distance to wall c=height of object d= height of object on wall so i plugged in 2.6m/1m = d/.217m so i got d=.564m i plugged that in and it said i was wrong.
 
dblader said:
im pretty sure that they would be equal. a=distance from source to object b=distance to wall c=height of object d= height of object on wall so i plugged in 2.6m/1m = d/.217m so i got d=.564m i plugged that in and it said i was wrong.

So what is the distance of the light to the wall again?
 
i figured it out. I took 1m+2.6m=3.6m*.217m=.781m which is the correct answer. but can you explain why that is i know how to do it know but i need to understand it. thanks for your help.
 
dblader said:
i figured it out. I took 1m+2.6m=3.6m*.217m=.781m which is the correct answer. but can you explain why that is i know how to do it know but i need to understand it. thanks for your help.

Similar triangles means the ratio of the complete side to complete side.

You were trying to compare a triangle to trapezoid.
 
okay so d is the whole side so when i was multiplying 2.6m it wasn't the whole side of the triangle but 3.6m is the whole side of the triangle. thanks
 

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