How Fast Does the Ladder Slide Down the Wall?

[ladyrae]

Use differentiation to solve the following

A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at rate of 2 feet per second. How fast is the top moving down the wall when the base of ladder is 15 feet from the wall.

What's the equation?

Thanks

 

[cookiemonster]

Use the Pythagorean Theorem.

x^2 + y^2 = z^2

Diffentiate:

x\frac{dx}{dt} + y \frac{dy}{dt} = z\frac{dz}{dt}

Solve for the desired variable, dy/dt in this case

\frac{dy}{dt} = \frac{z\frac{dz}{dt} - x\frac{dx}{dt}}{y}

Plug in values you know, using x^2 + y^2 = z^2 to determine distances you don't.

cookiemonster

 

[ladyrae]

how about this one

Using Differentiation solve

a rocket is launched vertically and is tracked by a radar station located on the ground 12 kilometers from the launch site. When the rocket is 20 km away from the radar station, its distance from the station is increasing at the rate of 2500 km/hr. What is the vertical speed of the rocket at this instant?

What is the equation?

Thanks

 

[Gokul43201]

Same approach as the previous problem. Now you know x, y and can find z from Pyth. What is important is understanding what dx/dt and dy/dt are equal to.

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