Calculus Word Problem: Finding Rate of a Sliding Ladder with Pythagoras Theorem

In summary, the problem involves a 15-foot ladder sliding down a vertical wall at a rate of 2 feet per minute. Using Pythagoras theorem and differentiating, we can find the rate at which the ladder is sliding down the wall when the bottom of the ladder is 9 feet from the base of the wall.
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Niaboc67
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Question: Suppose a 15-foot ladder is sliding down a vertical wall, with the bottom of the ladder sliding away from the wall at a rate of 2 feet per minute. Sketch a picture of the situation, with labels x and y indicating horizontal and vertical distances, respectively. Then find the rate at which the ladder is sliding down the wall when the bottom of the ladder is 9 feet from the base of the wall.

pretty sure I should use Pythagoras theorem to solve and solve but could use some help on how to figure this out. Thank you
 
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Niaboc67 said:
pretty sure I should use Pythagoras theorem to solve and solve but could use some help on how to figure this out. Thank you
Let distance of bottom of ladder from base of wall at any time be x . Then , let height of ladder be y .

Write pythagoras theorem . Differentiate ( You know x , dx/dt and y ) .
 

Related to Calculus Word Problem: Finding Rate of a Sliding Ladder with Pythagoras Theorem

1. What is a calculus word problem?

A calculus word problem is a type of mathematical problem that involves using calculus principles and techniques to solve a real-world scenario. These problems often involve finding rates of change, maximizing or minimizing a function, or determining the area under a curve.

2. How do I approach solving a calculus word problem?

The first step in solving a calculus word problem is to carefully read and understand the problem. Then, identify the given information and what you are being asked to find. Next, use your knowledge of calculus concepts and formulas to set up an equation or system of equations. Finally, solve the equations and check your answer to ensure it makes sense in the context of the problem.

3. What are some common strategies for solving calculus word problems?

Some common strategies for solving calculus word problems include drawing a diagram or graph to visualize the problem, breaking the problem down into smaller parts, and using calculus techniques such as derivatives and integrals to solve for the unknown variable.

4. Can calculus word problems be solved without using calculus?

In some cases, calculus word problems can be solved using algebra or other non-calculus methods. However, using calculus techniques can often provide a more efficient and accurate solution.

5. How can I check my answer for a calculus word problem?

To check your answer for a calculus word problem, you can plug your solution back into the original problem and see if it satisfies all the given conditions. You can also graph your solution and compare it to the graph of the original problem to see if they match.

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