A 20-foot ladder is leaning against a building. If the bottom of the ladder is s

Question

A 20-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 1 feet/second, how fast is the top of the ladder moving down when the foot of the ladder is 2 feet from the wall? The top of the ladder is moving down at a rate of feet/second when the foot of the ladder is 2 feet from the wall. (Round to the nearest thousandth as needed.) A rock is thrown into a still pond. The circular ripples move outward from the point of impact of the rock so that the radius of the circle formed by a ripple increases at the rate of 4 feet per minute. Find the rate at which the area is changing at the instant the radius is 6 feet. When the radius is 6 feet, the area is changing at approximately square feet per minute. (Round to the nearest thousandth as needed.) A pulley is on the edge of a dock, 7 feet above the water level. A rope is being used to pull in a boat. The rope is attached to the boat at water level. The rope is being pulled in at the rate of 2 feet per second. Find the rate at which the boat is approaching the dock at the instant the boat is 7 feet from the dock. The boat is approaching the dock at a rate of feet per second when the boat is 7 feet from the dock. (Round to the nearest thousandth as needed.)

Explanation / Answer

x2+y2=L2 differentiating both sides x.x'+y.y'=l.l' l'=2 , y=7, y'=0 ,x=7 solving we get l'=2.828= speed of the rope

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