Question

A ladder 8 meters long is leaning against a wall. If the top of the ladder is slipping down at the rate of 8 meters per second, how fast is the bottom moving away from the wall when it is 7 meters from the wall?

Please give your answer in , enter it without the units.

Answer 1

When the ladder base is 7m from the wall, the top is √(64-49) = √15 from the ground.

When the base is x meters from the wall,

x^2 + h^2 = 64
2x dx/dt + 2h dh/dt = 0
2(7)dx/dt + 2√15 (-8) = 0

dx/dt = 16√15/14 = 4.43m/s