A trouble como felong nike his minds shapļa ite is teeler Prangles five feet across the top and having height 1 foot. meme If water is poured into the trough at 15 cubic Feet per minute how fast is the water level rising when the water is five A inches deep? V: Ah 14H. 3. A light in a lighthouse 2000 m from a straight shoreline is rotating at 2 revolutions per minute. How fast is the beam moving along the shore when it passes a point 500 m from the point on the shore opposite the lighthouse? 4. A camera is filming a rocket launch. The camera located on the ground 150 meters from a launch pad and points toward the rocket. It adjusts its angle of elevation to the horizontal as the rocket rises vertically at a constant rate of 2 m/s. Find the rate of change of the angle when the rocket is 100 m above ground. When the rocket is 1.0 km above ground. What is the limit of the tracking rate as the height of the rocket tends to infinity? 5. A Ferris wheel is 40 ft in diameter and its center is 25 feet above ground. If the wheel rotates once every 2 minutes, how fast is a passenger rising when she is 35 feet above the ground? How fast is she moving horizontally? 6. A spherical satellite enters Earth's atmosphere and burns up at a rate that, at each instant, is proportional to its surface area. Assuming the satellite is a solid and always retains its spherical shape, show that the radius decreases at a constant rate. Hints: Volume of a cone is given by 1-12h where is tho rodinn of the