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

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.