Differentation

**caramelcake** · March 27th 2011, 01:51 AM

A ladder $AB$ of length $5$ metres has one end $A$ leaning against a vertical wall. The other end $B$ rests on horizontal ground. When $A$ is at a height of $4$ metres, it slides down the wall at a rate of $2 m/s$ . How fast is the other end, $B$ , sliding along the horizontal ground? Answer: $\frac{8}{3}m/s$

I'm confused by this question and do not know where to start. If I use the chain rule and write $\frac{dB}{dt} = \frac{dB}{dx} \times \frac{dx}{dt}$ , where $B$ is the length of the floor from the wall to point $B$ and where $t$ is the time, what would $x$ be?
I only know that when A is at a height of 4 metres, B must be at 3 metres away from the wall because of the pythagora's theorem.

Any help would be appreciated and thank you in advance.

**mr fantastic** · March 27th 2011, 02:24 AM

Originally Posted by caramelcake

I'm confused by this question and do not know where to start. If I use the chain rule and write $\frac{dB}{dt} = \frac{dB}{dx} \times \frac{dx}{dt}$ , where $B$ is the length of the floor from the wall to point $B$ and where $t$ is the time, what would $x$ be?
I only know that when A is at a height of 4 metres, B must be at 3 metres away from the wall because of the pythagora's theorem.

Any help would be appreciated and thank you in advance.

At time t, $B^2 + x^2 = 5^2$ ....

**caramelcake** · March 27th 2011, 05:22 AM

Originally Posted by mr fantastic

At time t, $B^2 + x^2 = 5^2$ ....

What does x here represent?

**skeeter** · March 27th 2011, 05:58 AM

Originally Posted by caramelcake

What does x here represent?

B is the distance from the wall to the foot of the ladder

5 is the length of the ladder

x is the distance from the wall to the top of the ladder

**mr fantastic** · March 27th 2011, 11:08 AM

Originally Posted by caramelcake

What does x here represent?

The whole point of questions like this is that you introduce variables and set up the equation. Why have you written down an equation involving a pronumeral x when you don't know what x is!! (I had asumed you did not know an expression for x, but did know what x represented since it was your symbol in your equation).

I think you need to go back to your class notes and textbook and review all the material and examples for related rates of change.

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