Problem

According to the model we used to solve Example 2…

06:02

Problem 33 Hard Difficulty

The top of a ladder slides down a vertical wall at a rate of $ 0.15 m/s. $ At the moment when the bottom of the ladder is $ 3 m $ from the wall, it slides away from the wall at a rate of $ 0.2 m/s. $ How long is the ladder?

Name: the top of a ladder slides down a vertical wall at a rate of 015 ms at the moment when the bottom of
Uploaded: 2021-02-10
Duration: 2 min 42 s
Channel: Numerade
Description: The top of a ladder slides down a vertical wall at a rate of $ 0.15 m/s. $ At the moment when the bottom of the ladder is $ 3 m $ from the wall, it slides away from the wall at a rate of $ 0.2 m/s. $ How long is the ladder?

Answer

5 $\mathrm{m}$

Grace H.

Caleb E.

Baylor University

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University

Watch More Solved Questions in Chapter 3

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Video Transcript

So in this problem, we want to know, um that when the bottom of the ladder is 3 m from the wall, we want to know how long the latter is given this information. So we have our ladder and we have our wall. Um, we know that the length of the latter l or right here l is constant. Um, we also know that since the latter is falling, we will have that d y d t is gonna be negative because it's going down like this. So we want to represent the length of the water is elsewhere being equal to X squared plus y squared. And that's just Pythagorean theorem. The idea that the high pop news is equal to the sum of the squares of the X direction and the Y direction. So with that in mind, we assume that the latter is going to be touching both surfaces. The coefficients of two when we take the derivative can just be divided off. So really, all that we're left with is that d l d t is equal to, um is equal. Thio two x dx DT plus two. I do y d t. But once again, as we suggested, we can get rid of those twos. So since, uh, the length is constant, what we really have is going to be zero equals x dx DT times Why or a plus y d Y d t So that's our first equation that we're gonna be using when we solve for why we end up getting that on plugging in the other values that we have, we get the zero is equal to three times point to plus why times negative 0.15 With that, we end up getting that since X is three in this case, that why is going to give us four now, Um, with this in mind, since we have are some of the values that we're looking to find, we know that we now have that three squared plus four squared because that's the X and Y values is going to equal r l squared. And we know that the answer to this because the +345 triangle is five. So the length of our ladder is 5 m

Carson M.

California Baptist University

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Calculus 1 / AB

Calculus: Early Transcendentals

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