Question

The top of a ladder 6 meters long is resting against a vertical wall.Suddenly , the ladder begins to slide outwards. At the instant when the foot of the ladder is 4 meters from the wall, it is sliding away at the rate of 0.5 m/ sec. How fast is the top sliding downward at this moment ?

Answer 1

$x^2+y^2=l^2$

x is the foot distance and y is the height at which top point of ladder touched wall

differentiate

$2x\frac{dx}{dt}=-2y\frac{dy}{dt}$

$x=4$

$l=6$

$\frac{dx}{dt}=0.5$

so $y=4.472$

$\frac{dy}{dt}=0.447$