SOLUTION: A 17 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how fast will the foot be moving away from the wall when the top is 14 feet above th

Question 1160398: A 17 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how fast will the foot be moving away from the wall when the top is 14 feet above the ground?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

x is the distance the foot of the 17-foot ladder is from the wall when the height the ladder reaches on the wall is y:

Differentiate to find the rate of change in x for the given rate of change in y.

Square the given equation to avoid differentiating the square root function.

dy/dt is given as -4 (ft/sec); when y=14, x is .

When the top of the ladder is 14 feet above the ground, the foot is moving away from the wall at a rate of 56/sqrt(93) ft/sec, or about 5.8 ft/sec.

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