1. ## Differentation

A ladder $\displaystyle AB$ of length $\displaystyle 5$ metres has one end $\displaystyle A$ leaning against a vertical wall. The other end $\displaystyle B$ rests on horizontal ground. When $\displaystyle A$ is at a height of $\displaystyle 4$ metres, it slides down the wall at a rate of $\displaystyle 2 m/s$. How fast is the other end, $\displaystyle B$, sliding along the horizontal ground? Answer: $\displaystyle \frac{8}{3}m/s$
I'm confused by this question and do not know where to start. If I use the chain rule and write $\displaystyle \frac{dB}{dt} = \frac{dB}{dx} \times \frac{dx}{dt}$ , where $\displaystyle B$ is the length of the floor from the wall to point $\displaystyle B$ and where $\displaystyle t$ is the time, what would $\displaystyle x$ 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.

2. 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 $\displaystyle \frac{dB}{dt} = \frac{dB}{dx} \times \frac{dx}{dt}$ , where $\displaystyle B$ is the length of the floor from the wall to point $\displaystyle B$ and where $\displaystyle t$ is the time, what would $\displaystyle x$ 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, $\displaystyle B^2 + x^2 = 5^2$ ....

3. Originally Posted by mr fantastic
At time t, $\displaystyle B^2 + x^2 = 5^2$ ....
What does x here represent?

4. 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

5. 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.