1. A ladder 20ft long is leaning against a wall inclined 60 to the horizontal. If the bottom of the ladder is being moved horizontally toward the wall at ift/sec, how fast is the top of the ladder moving when the bottom is 4ft from the wall? 2. Sand is being dropped at a rate of 10m /min onto a conical pile. If the height of the pile is always twice the base radius, at what rate is the height increasing when the pile is 8m high? 3. A stone is dropped into a still pond. Concentric circular ripples spread out, and the radius of the disturbed region increases at the rate of 16 cm/sec. At what rate does the area of the disturbed region increases when its radius is 4cm? 4. An automobile traveling at a rate of 30ft/secs approaching an intersection. When the automobile is 120ft from the intersection, a truck traveling at the rate of 40ft/sec crosses the intersection. The automobile and the truck are on roads that are at right angles to each other. How fast are the automobile and the truck separating 2sec after the truck leaves the intersection?