Question

8. A 20-ft ladder is placed against a building resting on a banana peel. The base of the ladder is slipping away from the building at a rate of 1.5-ft/min. Find the rate at which the top of the ladder is siding down the building at the instant the bottom of the ladder is 12-ft from the base of the building.

Answer 1

tength of ladder = 20 ft. y st 5 202-18 Z Now y= When a = 12ft y Thoo-(12² 400-144 = 256 Or ye 16.0ft theorem, Using Pythagorus t²t 2 ty 202 =) d (xity)(2012 Differentialing both sides wat it at 1 at a time instant

2x dx + 2y dy zy dy = 0 at or 2 x da at - 2y dy at - 2x adx or dy 是上 at 24 프 x dx = 12 x 1.5 16 dy = - 1.125 ft/min de T Therefore, the ladder is sliding the building at the rate of 1-1.125