Related Rates Question: How to Use Similar Triangles to Solve for Shadow Length?

In summary, the question is asking for the rate at which the man's shadow on the building is becoming shorter when he is 20ft from the building. To solve this problem, we can use similar triangles and the given information to find the height of his shadow as a function of his distance from the building. Once we have this function, we can find the derivative and plug in the value of x to get the answer of -3.6ft/s.
  • #1
jen333
59
0
Hey, I have this one practise calculus question that I just can't seem to get. Any help would be greatly appreciated:

A light is on the ground 40ft from a building. A man 6ft tall walks from the light towards the building at 6ft/s. How rapidly is his shadow on the building becoming shorter when he is 20ft from the building?
(btw, the answer should be -3.6ft/s)

I've already drawn a diagram, but I'm not sure if triangle ratios would do any good.
 
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  • #2
Were you able to find the height of his shadow as a function of his distance from the building?
 
  • #3
First draw a picture. You know its going to be a triangle. Let x be the distance the man is from the light. And let y be the height of his shadow on the building. You know dx/dt = 6. We also know that the length of the triangle is 40 ft. So we can divide the side into x + (40-x). So how would you use similar triangles to find y as a function of x?

Hint: [tex] \frac{6}{x} = \frac{y}{?} [/tex]
 
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FAQ: Related Rates Question: How to Use Similar Triangles to Solve for Shadow Length?

1. What are related rates questions?

Related rates questions are problems in calculus that involve finding the rate of change of one quantity with respect to another. These problems typically involve multiple variables and require the use of derivatives to solve.

2. How do I solve a related rates question?

To solve a related rates question, you must first identify the variables involved and the relationship between them. Then, use the given information and the chain rule to set up an equation relating the rates of change. Finally, use calculus techniques to solve for the desired rate of change.

3. What are some common examples of related rates problems?

Some common examples of related rates problems include rates of change involving geometric shapes (such as a changing radius of a circle), rates of change involving volumes and areas (such as a leaking tank), and rates of change involving motion (such as a moving car).

4. What are some tips for solving related rates questions?

Some tips for solving related rates questions include drawing a diagram to visualize the problem, labeling all known and unknown variables, and carefully applying the chain rule to set up the equation. It is also important to pay attention to units and use proper notation.

5. How can I check if my answer to a related rates question is correct?

The best way to check the correctness of your answer to a related rates question is to go through the problem again and make sure all of the given information and equations were correctly used. You can also plug your answer back into the original equation and see if it satisfies the conditions of the problem.

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