Rate of change of the area of the rebgion

[fifaking7]

Homework Statement

A board 5 feet long slides down a wall. at the instant the bottom end is 4 feet from the wall, the other end is moving down the wall the rate of 2 feet per second.at that moment how fast is the area of the region between the board, the ground and the wall changing?

Homework Equations

a=1/2bh

The Attempt at a Solution

x^2 + 4^2= 5^2
x=3
da/dt= 1/2b(db/dt)(dh/dt)

I think i started it up wrong and I don't know where to go next..

 

[SammyS]

Homework Statement

A board 5 feet long slides down a wall. at the instant the bottom end is 4 feet from the wall, the other end is moving down the wall the rate of 2 feet per second.at that moment how fast is the area of the region between the board, the ground and the wall changing?

Homework Equations

a=1/2bh

The Attempt at a Solution

x^2 + 4^2= 5^2
x=3
da/dt= 1/2b(db/dt)(dh/dt)

I think i started it up wrong and I don't know where to go next..

What is the shape of the region below the board and above the ground at the moment under consideration?

 

[fifaking7]

just a normal triangle drawn on a line like a typical triangle leaning against a wall problem.

 

[SammyS]

Neither end of the board is touching the ground, so it's not a triangle.

 

[aralbrec]

Homework Equations

a=1/2bh

da/dt= 1/2b(db/dt)(dh/dt)

Have another look at that derivative. It looks like the product rule hasn't been applied properly. Also one of those b/h is x. You'll have to stay consistent with your variable names.

 

[fifaking7]

http://img231.imageshack.us/img231/5130/scan0060kd.jpg

that is how it looks

 

[SammyS]

http://img231.imageshack.us/img231/5130/scan0060kd.jpg

that is how it looks

You're right. I misread the problem.

When you said x=3, that should be h=3 .

In general, how are b and h related, considering that they're legs of a right triangle?

 

[fifaking7]

i said b= 4ft and h=3 ft

 

[SammyS]

i said b= 4ft and h=3 ft

That's what b & h are at the instant that h = 4 ft, but how are they related in general?

(Use the Pythagorean theorem.)

 

[Ray Vickson]

i said b= 4ft and h=3 ft

The crucial point that you seem to be missing is that you need to figure out what is happening as the board slides down the wall, so h moves from more than 3 ft to less than 3 ft (and, at the same time, b moves from less than 4 ft to more than 4 ft). When that is happening, the area of the triangle is changing, and that is what you are supposed to be reckoning. So, you need to let b and h be variables, not fixed numbers.

RGV

 

[SammyS]

That's what b & h are at the instant that h = 4 ft, but how are they related in general?

(Use the Pythagorean theorem.)

Of course, that's a typo !

It should have said:

That's what b & h are at the instant that b = 4 ft, but how are they related in general?
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