Calculating Tree Height: Using a Plane Mirror to Measure 205m

In summary, by setting up a ratio and solving for the height of the tree based on the given information, the height of the tree is determined to be 205 meters. However, this answer is not correct. A more accurate method would be to draw a ray diagram, where the rays from the top and bottom of the tree just touch the top and bottom of the mirror respectively, and then extend those lines past the mirror to the distance of the viewer's eye.
  • #1
Punkyc7
420
0
the image of a tree just covers the length of a plane mirror 4.3 cm tall when the mirror is held 32 cm from the eye. The tree is 28 m from the mirror.

What is the height of the tree?


so I set up a ratio

.043/.32=(28-.32)/h

and solved for h and got 205 meters, but I am not sure if that is correct.
 
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  • #2
No, 205 meters is not correct.

Draw a ray diagram. A ray from the top of the tree should just touch the top of the mirror. Another ray from the bottom of the tree should just touch the bottom of the mirror. The rays reflecting from the mirror surface, we are told, come together at the distance of the viewer's eye, some 32cm in front of the mirror.

What would happen if you were to extend the lines of those rays past the mirror?
 

1. How was the height of this tree measured?

The height of this tree was measured using advanced laser technology called LiDAR (Light Detection and Ranging) which uses high intensity laser pulses to accurately measure the distance to objects.

2. What is the average height of trees?

The average height of trees varies greatly depending on the species, location, and age of the tree. However, on average, trees range from 10-30 meters in height.

3. How does this tree compare to other tall trees in the world?

This tree is considered one of the tallest trees in the world, with some of the tallest trees reaching heights of over 115 meters. However, the exact ranking of this tree may vary as new trees are constantly being discovered.

4. What factors contribute to a tree's height?

The height of a tree is influenced by a variety of factors, including genetics, environment, and access to resources such as water and nutrients. Additionally, some species have evolved to grow taller in order to compete for sunlight in dense forests.

5. Can trees continue to grow taller?

Yes, trees have the potential to continue growing taller throughout their lifespan, but the rate of growth may slow down as they age. Some species have been known to grow taller than 100 meters, but it is rare for a tree to reach heights of over 200 meters.

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