22 Nov '05 22:41

Suppose you have a ladder of length "L" sitting on a frictionless floor, leaning up against a frictionless wall, held in place by a doorstop-like buttress (heheh, buttress...). The height of the ladder against the wall "h" is given by the following formula:

x^2 + h^2 = L^2

where "x" is the distance from the wall to the foot of the ladder. If you remove the buttress and drag the foot of the ladder away from the wall at a constant velocity "k", we can find the change in height of the top of the ladder with time (vertical velocity) by taking the derivative of the

above formula:

2x*(dx/dt) + 2h*(dh/dt) = 2L*(dL/dt)

which simplifies to:

2xk + 2h*(dh/dt) = 0

and solving for (dh/dt):

(dh/dt) = -xk/h

As the height of the ladder approaches zero, the magnitude of the vertical velocity (the speed) approaches infinity. Is this possible? If not, where is the mistake in the above problem statement (he asked knowingly)?

x^2 + h^2 = L^2

where "x" is the distance from the wall to the foot of the ladder. If you remove the buttress and drag the foot of the ladder away from the wall at a constant velocity "k", we can find the change in height of the top of the ladder with time (vertical velocity) by taking the derivative of the

above formula:

2x*(dx/dt) + 2h*(dh/dt) = 2L*(dL/dt)

which simplifies to:

2xk + 2h*(dh/dt) = 0

and solving for (dh/dt):

(dh/dt) = -xk/h

As the height of the ladder approaches zero, the magnitude of the vertical velocity (the speed) approaches infinity. Is this possible? If not, where is the mistake in the above problem statement (he asked knowingly)?