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AP Calculus AB Lesson 22 on Related Rates Problems Day 3 p. 1 Related Rates Problems Where The Angle Is Changing: Example 1: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1 ft/s, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 ft from the wall? Recall Answer from Example 2 of first day of related rates was -0.75 ft/sec. New question: How fast is the angle with the horizontal changing when the bottom of the ladder is 6 ft from the wall? Example 2: An airplane, flying at 450 km/hr at a constant altitude of 5 km, is approaching a camera mounted on the ground. Let be the angle of elevation above the ground at which the camera is pointed. When = , how fast does the camera have to rotate in order to keep the plane in 3 view? AP Calculus AB Lesson 22 on Related Rates Problems Day 3 p. 2 Example 3: A kite 100ft above the ground moves horizontally at speed of 8ft/sec. At what rate is the angle between the string and the horizontal decreasing when 200 ft of string has been let out? Example 4: A lighthouse is located on a small island 3 km away from the nearest point P on a straight shoreline and its light makes the four revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P? Homework p. 212 ( 24, 27)