Thursday

March 5, 2015

March 5, 2015

Posted by **Johnny** on Thursday, November 8, 2012 at 6:37am.

a. How fast is the top of the ladder moving down the wall at that moment?

b. At what rate is the area of the triangle formed by the ladder, wall, and ground changing at the moment?

c. At what rate is the angle between the ladder and the ground changing at that moment?

I wasn't here the day the teacher taught us this...plz help me i have no idea where to start

- Calculus -
**Steve**, Thursday, November 8, 2012 at 10:54amThis is just an exercise in implict differentiation.

At the moment in question, we have a 24-32-40 right triangle, with height=24.

Let θ be the angle between the ladder and the ground.

Let the base be x, and the height be y.

a)

x^2 + y^2 = 40^2

2x dx/dt + 2y dy/dt = 0

when x=32,

2(32)(4) + 2(24) dy/dt = 0

dy/dt = -16/3

so, the top is sliding down at 16/3 ft/s

b)

a = 1/2 xy

da/dt = 1/2 (y dx/dt + x dy/dt)

da/dt = 1/2 (24(4) + 32(-16/3))

= -112/3 ft^2/s

c)

y/x = tanθ, so

y = x tanθ

dy/dt = tanθ dx/dt + x sec^2θ dθ/dt

-112/3 = 3/4 (4) + 32 (5/4)^2 dθ/dt

dθ/dt = -121/150 rad/s

**Answer this Question**

**Related Questions**

Calculus - A 13 foot ladder is leaning against the house when it's base starts ...

AICE math - A 30 foot ladder is leaning against a house(see figure). if the base...

Calculus Please Help!! - "A 13-foot ladder is leaning against a building when ...

CALCULUS HELP!! - I haven't done this type of problem in a while, so if someone ...

math - a 15 foot ladder is leaning against a house with the base of the ladder 4...

Math - A ladder is leaning against the side of a house so that it can reach a ...

Geometry - A 12 foot ladder is leaning against a house. If the top of the ladder...

geometry - A painter leans a 15 ft ladder against a house. The base of the ...

calculus - A 13 ft ladder is leaning against a house when its base begins to ...

math - A ladder is leaning against the side of a house and forms an angle of 66o...