Differentiation and Related Rates
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Please use differentiation and related rates to solve the following problems. Please explain answers and solve to specified solutions.
A Ladder is 25 feet long and is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second.
(a) How fast is the top moving down the wall when the base of the ladder is 7 feet, 15 feet and 24 feet from the wall?
(b) Consider the triangle formed by the side of the house, the ladder and the ground. Find the rate at which the area of the triangle is changing when the base of the ladder is 7 feet from the wall.
(c) Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 7 feet from the wall.
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Solution Summary
A ladder placed against a vertical wall and the lower end is pulled. The velocity of the upper end, the rate of change of area of the triangle formed and the angular velocity is calculated.
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