refer to a 5-meter ladder sliding down a wall, as in Figures 1 and 2. The variable h is the height of the ladder’s top at time t, and x is the distance from the wall to the ladder’s bottom.

10. Suppose that the top is sliding down the wall at a rate of 1.2 m/s. Calculate dx/dt when h = 3 m.

Question

refer to a 5-meter ladder sliding down a wall, as in Figures 1 and 2. The variable h is the height of the ladder’s top at time t, and x is the distance from the wall to the ladder’s bottom.

10. Suppose that the top is sliding down the wall at a rate of 1.2 m/s. Calculate dx/dt when h = 3 m.

anonymous · Answer

You already know dh/dt. (it is 1.2) You want to know dx/dt

using chain rule,
$$\frac{dx}{dt}=\frac{dx}{dh}*\frac{dh}{dt}$$
what you don't know, is dx/dh. Find that and you can solve it.

To find dx/dh, use the pythagorean theorem to find the relationship between x and h, then find the derivative of that.