Related rates problem, Find the velocity of the top of the ladder

Question

A 20 ft ladder leans against a wall. The bottom of the ladder is 4 ft from the wall at time 𝑡=0 and slides away from the wall at a rate of 1ft/sec. Find the velocity of the top of the ladder at time t=3

I got (sqrt(6))/(6) but it's incorrect

Answer 1

Related rate problem: let y be the height that the ladder touches on the wall, x be distance of the ladder along the floor from the wall. The relationship of y and x is obtained using the Pythagorean Theorem:

y = sqrt(20^2 - x^2) = sqrt(400 -x²)

Differentiating in t:

dy/dt = 1/2 (400 - x²)^-1/2 (-2x dx/dt) = -x(400 - x²)^-1/2 dx/dt

dy/dt ( @3 s) = - (400ft² - (7ft)²)^-1/2(7ft)(1ft/s) = -.374 ft/s (note x(@3s) = 4 ft + 3s(1ft/s))

Hope that helps.