A ladder 10 metres long is leaning versus a vertical wall. If the bottom the the ladder is traction horizontally far from the wall surface at the rate of 1.2 metres per second, discover how quick the top of the ladder is sliding down the wall, as soon as the bottom is 6 metres far from the wall.

You are watching: A ladder 10 meters long is leaning

Let ab be the ladder, where abdominal = 10 meters. Let in ~ time t seconds, the finish A the the ladder be x metres from the wall and the end B be y metres from the ground.

Since, OAB is a right angled triangle, through Pythagoras theoremx2 + y2 = 102i.e. Y2 = 100 – x2Differentiating w.r.t. T, we get

`2ydy/dt = 0 - 2xdx/dt`

∴ `dy/dt = x/y.dx/dt` ...(1)

Now, `dx/dy = (12"metres")/sec` is the price at wh the bottom that the ladder s traction horizontally and `dy/dx` is the price which the optimal of ladder B is sliding.

See more: What'S Good For Goose Good For Gander Meaning, What'S Good For The Goose

which the height of ladder B is sliding.When x = 6, y2 = 100 – 36 = 64∴ y = 8

∴ (1) gives, `dy/dx = -(6)/(8)(1.2)`

= `(6)/(8) xx (12)/(10)`

= `-(9)/(10)`

= – 0.9Hence, the top of the ladder is sliding down the wall, at the rate of `(0.9"metre")/sec`.

Concept: Derivatives together a price Measure

Report ErrorIs over there an error in this concern or solution?

Chapter 2: Applications the Derivatives - exercise 2.1

Q 15Q 14Q 16

APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th typical HSC Maharashtra State Board

Chapter 2 Applications that DerivativesExercise 2.1 | Q 15 | web page 72

Advertisement eliminate all ads

Question bank with Solutions

Textbook Solutions

NCERT Solutions

Board/University study Material

Question record Solutions

Other Resources

© 2021 stclairdrake.net | contact Us|Privacy Policy

Share

0

0

0

0

0

Notifications

View all notifications

Select a course

CANCEL

My Profile

My profile

why create a file on stclairdrake.net? 1. Notify you about time table the exam. 2. Educate you about new question papers. 3. Brand-new video tutorials information.Login / Register

S

user

Login

Create free account

- or -

Course

HSC arts 12th Board exam Maharashtra State Board

HSC science (General) 12th Board test Maharashtra State Board

HSC scientific research (Computer Science) 12th Board exam Maharashtra State Board

HSC science (Electronics) 12th Board test Maharashtra State Board

change

Change modeLog out

View in app×