A 25-foot ladder is leaning against a house. The base of the ladder is pulled aw

Question

A 25-foot ladder is leaning against a house. The base of the ladder is pulled away from the house at a rate of 2 feet per second. How fast is the top of the ladder moving down the wall when the base is given below?

(a) 15 feet away from the house
ft/sec

(b) 20 feet away from the house
ft/sec

(c) 24 feet away from the house
ft/sec

A 25-foot ladder is leaning against a house. The base of the ladder is pulled away from the house at a rate of 2 feet per second. How fast is the top of the ladder moving down the wall when the base is given below? (a) 15 feet away from the house ft/sec (b) 20 feet away from the house ft/sec (c) 24 feet away from the house ft/sec

Explanation / Answer

let hight =x so x^2+y^2=25^2 so 2x dx/dt=-2ydy/dt so x dx/dt=-y dy/dt now a)x=15 ; y=20 so dy/dt=-x/y * dx/dt=-1.5 ft/s [ - for downwards] b)x=20;y=15 dy/dt=-x/y * dx/dt=-2.67 ft/s^2[- for downwards] c)x=24 so y=7 so dy/dt=-x/y * dx/dt=-6.86 ft./s

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