Question

A ladder 26ft long leans against a vertical wall. The lower end is being moved away from the wall at a rate of 5ft/sec how fast is the top decreasing when the lower end is 10 ft. from the wall

Answer 1

Let the length of the wall be l = 26ft, the distance of the lower end of the ladder from the wall be x and the height of the top of the ladder from the ground be y, then
l = sqrt(x^2 + y^2) = 26
x^2 + y^2 = 26^2 = 676
y^2 = 676 - x^2
y = sqrt(676 - x^2)
dy/dt = -2x dx/dt / 2sqrt(676 - x^2) = -2(10)(5) / 2sqrt(676 - (10)^2) = -100 / 48 = -2.083 ft/sec.