Calculating Tree Height with a 5cm Mirror

In summary, a 5cm mirror held 20 cm away from the eye of an observer who is 100 m away from a tree is able to show the whole image of the tree. The height of the tree can be determined by drawing the image using the mirror, eye, and tree as reference points.
  • #1
sofianets
3
0

Homework Statement



A 5cm mirror is just large enough to show the whole image of a tree when held 20 cm from the eye of the observer whose distance to the tree is 100 m. What is the height of tree?


Homework Equations



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The Attempt at a Solution



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  • #2
welcome to pf!

hi sofianets! welcome to pf! :smile:
sofianets said:
A 5cm mirror is just large enough to show the whole image of a tree when held 20 cm from the eye of the observer whose distance to the tree is 100 m. What is the height of tree?

start by drawing the image :wink:

(and the mirror and the eye and the tree, of course)
 

Related to Calculating Tree Height with a 5cm Mirror

What is the purpose of calculating tree height with a 5cm mirror?

The purpose of calculating tree height with a 5cm mirror is to accurately measure the height of a tree without having to physically climb or measure it. This method uses simple geometry and the principles of similar triangles to determine the height of the tree.

What materials are needed to calculate tree height with a 5cm mirror?

To calculate tree height with a 5cm mirror, you will need a 5cm mirror, a meter stick or measuring tape, a calculator, and a clear line of sight to the top of the tree. It is also helpful to have a partner to assist with measuring and holding the mirror.

How does the 5cm mirror method work?

The 5cm mirror method works by using the principle of similar triangles. By measuring the distance from the tree to the mirror and the distance from the mirror to the ground, you can create a proportion that can be solved to determine the height of the tree. The mirror acts as the top point of the triangle, and the distance from the mirror to the ground is the base of the triangle. The tree's height is the missing side of the triangle.

Is the 5cm mirror method accurate for all types of trees?

The 5cm mirror method is generally accurate for most types of trees. However, it may not work as well for trees with irregular shapes or those that are leaning. It is best to use this method on trees with a straight and consistent trunk.

Are there any safety precautions to consider when using the 5cm mirror method?

Yes, it is important to take safety precautions when using the 5cm mirror method. Be sure to have a partner to assist and always be aware of your surroundings, especially if you are near a busy road or in a densely wooded area. It is also important to use caution when holding the mirror and avoid looking directly into the sun's reflection.

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