Question

A 25m ladder is leaning against a
vertical wall. The floor is s
lightly slippery and the foot
of the ladder slips away from the wall at a rate of 0.3m/
s. How fast is the top of the l
adder sliding down the wall when the top is 20m above the floor?

Answer 1

if the base of the ladder is x from the wall, and the height up the wall is y, then we have

x^2+y^2 = 25^2
so, when y=20, x=15.

Taking the derivative wrt t, we have

x dx/dt + y dy/dt = 0

Now just find dy/dt, knowing that dx/dt = 0.3

Note that dy/dt will be negative, since the top is sliding down.

Answer 2

x^2+y^2=25^2
2x+2y.dy/dx=0
dy/dx=-x/y
dy/dt=dx/dt.dy/dx
=(0.3).(-x/y)
=(0.3).(-15/20)
=-0.225m/s