Related rates problem help

In summary: The important thing to note is that the top of the ladder is sliding down the wall at a rate of -17.5 cm per second. This is the answer to the problem. In summary, the top of the ladder is sliding down the vertical wall with a speed of -17.5 cm per second.
  • #1
53Mark53
52
0

Homework Statement


laddercopy.png


A 1.9 metre ladder is leaning against a vertical wall. If the bottom of the ladder is 30 cm from the wall and is being pull away from the wall with a horizontal speed of 25 cm per second, how fast is the top of the ladder sliding down the vertical wall?

We define the the direction up the wall to be positive, so that your answer must be negative.

Homework Equations


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does this mean when x=30 cm dx/dt = 25

The Attempt at a Solution


[/B]
this means that the wall height is 187.6 cm using pythagoras theorem

Any help will be much appreciated
 
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  • #2
53Mark53 said:
does this mean when x=30 cm dx/dt = 25
Yes. Start with writing height of the ladder as a function of x.
 
  • #3
cnh1995 said:
Yes. Start with writing height of the ladder as a function of x.

does this mean

h=x^2+y^2

dx/dt=2x+2y

25=2x30+2y
-35=2y
y=-17.5
 
  • #4
cnh1995 said:
Yes. Start with writing height of the ladder as a function of x.

I got the answer thanks :)
 
  • #5
Height of the ladder is h=√(L2-x2), where L=length of the ladder i.e. 1.9m.
You can proceed by taking derivative on both sides w.r.t. time.
 
  • #6
53Mark53 said:
this means that the wall height is 187.6 cm using pythagoras theorem
The height of the wall is irrelevant to this problem.
 

1. What is a related rates problem?

A related rates problem is a type of mathematical problem in which the rates of change of two or more related quantities are given, and the rate of change of a third quantity is sought. It involves using the chain rule to find the derivative of the dependent variable with respect to time.

2. How do I solve a related rates problem?

To solve a related rates problem, you need to follow these steps:

  1. Identify the given rates and the rate you are trying to find.
  2. Draw a diagram and label the variables.
  3. Write an equation that relates the given rates and the rate you are trying to find.
  4. Use the chain rule to differentiate the equation with respect to time.
  5. Substitute in the given values and solve for the rate you are looking for.

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

Some common examples of related rates problems include:

  • Filling a conical tank with water and finding the rate at which the water level is rising.
  • A ladder sliding down a wall and finding the rate at which the top of the ladder is moving.
  • A balloon inflating and finding the rate at which the radius is increasing.
  • A light post casting a shadow and finding the rate at which the length of the shadow is changing.

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

Here are some tips to keep in mind when solving related rates problems:

  • Draw a clear diagram and label the variables to help visualize the problem.
  • Write down the given rates and the rate you are trying to find before starting to solve.
  • Always use the chain rule to differentiate the equations.
  • Substitute in the given values as soon as possible to avoid mistakes.
  • Check your units to ensure they are consistent throughout the problem.
  • When in doubt, break the problem down into smaller parts and solve them individually.

5. Are there any common mistakes to avoid when solving related rates problems?

Some common mistakes to avoid when solving related rates problems include:

  • Forgetting to use the chain rule when differentiating.
  • Not labeling the variables correctly or not drawing a diagram.
  • Forgetting to substitute in the given values or substituting in the wrong values.
  • Mixing up the independent and dependent variables.
  • Not checking for units or using inconsistent units.
  • Making arithmetic or algebraic errors.

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