Decreasing size of person's shadow as they walk toward a lamp

In summary, the problem involves a man of height 6ft moving towards a lamp hanging at a height of 15ft with a velocity of 5ft/sec. The question is asking at what rate his shadow will decrease. The solution may involve using dynamic equations and a drawing to determine the length of the shadow in terms of the man's position and the heights of the lamp and man.
  • #1
Akash47
53
5
Member advised that effort must be shown at a solution attempt.

Homework Statement


If a man of height 6ft moves with 5ft/sec velocity towards a lamp hanging at 15ft height, then at what rate his shadow will decrease?

Homework Equations


Not sure but dynamic equations can help.

The Attempt at a Solution


I have no idea about how I can approach.So I want some ideas to reach the solution.
 
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  • #2
Akash47 said:

Homework Statement


If a man of height 6ft moves with 5ft/sec velocity towards a lamp hanging at 15ft height, then at what rate his shadow will decrease?

Homework Equations


Not sure but dynamic equations can help.

3. The attempt at a
Evolution

I have no idea about how I can approach.So I want some ideas to reach the solution.
A drawing will help. Can you find the length of the shadow (s) in terms of the position of the man (x), and the heights H and h?

upload_2018-11-6_15-1-44.png
 

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  • #3
Put the lamp at X=0, Y=15.
The position of the man will be X.
 

What causes a person's shadow to decrease in size as they walk toward a lamp?

The decrease in size of a person's shadow as they walk toward a lamp is due to the angle of light. As the person moves closer to the lamp, the angle of light between the person and the light source becomes smaller. This results in a smaller shadow being cast.

Why does the size of a person's shadow change?

The size of a person's shadow changes because of the distance between the person and the light source. The closer the person is to the light source, the smaller the shadow will be. This is due to the angle of light becoming smaller as the person moves closer to the light source.

Does the size of the light source affect the size of a person's shadow?

Yes, the size of the light source can affect the size of a person's shadow. A larger light source will result in a larger shadow, while a smaller light source will result in a smaller shadow. This is because a larger light source will cast a wider angle of light, resulting in a larger shadow.

Can a person's shadow disappear completely?

No, a person's shadow cannot disappear completely. As long as there is a light source, there will always be a shadow. However, the size and darkness of the shadow may decrease to the point where it is barely visible.

Why do shadows get shorter during the day?

Shadows get shorter during the day because of the movement of the sun. As the sun moves overhead, the angle of light changes, resulting in shorter shadows. This is why shadows are longest in the morning and evening, when the sun is closer to the horizon.

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