A 17 foot ladder is placed against a wall. if the foot of the ladder is pushed toward the wall at 0.5 feet per second, how fast is the top of the ladder rising when the foot is 8 feet from the wall?

Answer 1

at the moment in question, the height is 15. If the base of the ladder is x from the wall, and the height is y,

x^2+y^2 = 17^2
2x dx/dt + 2y dy/dt = 0
2(8)(-.5) + 2(15) dy/dt = 0
dy/dt = 4/15