A 16 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 15 feet above the ground?

Answer 1

x^2 + y^2 = 16^2 = 256
2 x dx/dt + 2 y dy/dt = d 256 /dt = 0
at start y = 15 so x = sqrt (256-225) = sqrt 31 = 5.568
11.14 dx/dt + 30 dy/dt = 0
dy/dt = -4 given so
11.14 dx/dt = -30 * -4 = +120 ft/s
dx/dt = 120/11.14
about 10.8 ft/s