A ladder rests against a vertical pole. The foot of the ladder is sliding away from the pole along horizontal ground. Find the inclination of the ladder to the horizontal at the instant when the top of the ladder is moving 3 times as

Question

fast as the foot of the ladder.

Answer 1

If the ladder has length z, then

x^2+y^2 = z^2
x dx/dt + y dy/dt = 0
when dy/dt = -3 dx/dt,
x dx/dt - 3y dx/dt = 0
x = 3y

Thus, the angle θ is

tanθ = 1/3