Question

A 16-foot ladder is resting against a wall when the bottom of the ladder begins to slip from the wall at a rate of 0.75 ft/s. Find the rate at which the top of the ladder is sliding down the wall when the bottom of the ladder is 10 ft away from the wall.

Answer 1

To find the rate at which the top of the ladder is sliding down the wall, we can use similar triangles. By using the Pythagorean theorem to find the length of the ladder and then applying the concept of similar triangles, we can determine that the rate at which the top of the ladder is sliding down the wall is approximately 0.936 ft/s.

Step-by-step explanation:

To find the rate at which the top of the ladder is sliding down the wall, we can use similar triangles. The ladder forms a right triangle with the wall, so we can use the Pythagorean theorem to find the length of the ladder when the bottom is 10 ft away from the wall:

a² + b² = c²

10² + b² = 16²

b² = 256 - 100

b = sqrt(156) ≈ 12.49 ft

Next, let's find the rate at which the bottom of the ladder is moving:

dB/dt = 0.75 ft/s

Finally, we can calculate the rate at which the top of the ladder is sliding down the wall using similar triangles:

dT/dt = (dB/dt * T) / B

dT/dt = (0.75 ft/s * 12.49 ft) / 10 ft ≈ 0.936 ft/s

Answer 2

8 feet from the wall.