Relates Rates hw question

Question

 A 12 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 2 ft/s, how fast will the foot be moving away from the wall when the top is 7 feet above the ground?

The foot will be moving at _______ ft/s

Answer 1

12^2 - 7^2 = 144 - 49 = 95 = b^2

b = sqr95

d^2 = h^2 + b^2

2dd' = 2hh' + 2bb'

dd' = hh' + bb'

12(0) = 7(-2) - sqr95(b')

b' = -14/sqr95 = -14sqr95/95 = about -1.44 ft/sec = rate of change of ladder's foot length from the bottom of the wall

in one second the top of the ladder will be at a height of 5 feet. 7-2 = 5

in one second the bottom of the ladder will be about sqr95 - 1.44 = about 8.31 feet from bottom of the wall.

5^2 + 8.31^2 = almost 95. The instantaneous rate of change about 1.44 ft./sec., close to the rate of change for 1 second.