Minimum length of the mirror required for a man to see the wall behind him?

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Homework Help Overview

The problem involves determining the minimum length of a mirror required for a man to see the wall behind him in a room of specific dimensions. The man has a height of 2h, the room length is 6h, and the wall height is 4h.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the conditions necessary for the man to see the entire wall, with one suggesting the use of a diagram to visualize the problem. There are inquiries about the approach to solving the problem and the necessary conditions that must be met.

Discussion Status

Some participants have offered guidance on how to approach the problem, including drawing diagrams and considering geometric relationships. There is a mix of attempts to clarify the problem and requests for help, indicating an ongoing exploration of the topic.

Contextual Notes

Forum rules emphasize that participants must find the solution themselves, which has led to some expressions of frustration regarding the need for assistance. There is also mention of a specific answer that one participant claims to have, though this is not universally accepted.

Lakshya
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A man of height 2h stands in the middle of a room of length 6h. The height of a wall is 4h. What is the minimum length of a mirror to be placed on the wall in front of the man so that he can see the entire wall behind him?
 
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Lakshya said:
A man of height 2h stands in the middle of a room of length 6h. The height of a wall is 4h. What is the minimum length of a mirror to be placed on the wall in front of the man so that he can see the entire wall behind him?

What is your approach to the problem? What conditions have to be met?
 
LowlyPion said:
What is your approach to the problem? What conditions have to be met?
The question is clear as it is. By the way, the answer is (4/3)h. I want the solution.
 
Lakshya said:
The question is clear as it is. By the way, the answer is (4/3)h. I want the solution.

Forum rules are you will have to find the solution yourself.

I was offering to help. If you need help, you can explain what you've done.

As to the answer, I already had that.
 
LowlyPion said:
Forum rules are you will have to find the solution yourself.

I was offering to help. If you need help, you can explain what you've done.

As to the answer, I already had that.

Yes, I need help. Tell me how to solve this problem. I don't know even a bit how to solve it.
 
Lakshya said:
Yes, I need help. Tell me how to solve this problem. I don't know even a bit how to solve it.

I would suggest that you draw a diagram with the viewer in the middle of the room at 3H. Divide the room vertically in half at 2H (to solve the top half which we can then double) with the eye level at 2H high now, the ray trace should go from that mid-point to one wall above the 2H level that reflects back to the top of the wall behind the viewer another 6H away. That total distance describes a triangle (if you unfolded the trip to and from that is 9H long and 2H high.

Since it is a similar triangle, the distance at the wall (the top height of the mirror) is to 3H as 2H is to 9H

X/3H = 2H/9H
X = 2H/3

Your final answer is 4H/3
 

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