Supposedly easy question, at what speed does the plank hit the floor? A plank of length 6 is standing against the wall. The distance from the bottom of the wall and the plank is given by $u = 2.5 + 0.01t$, that is, it is initially at distance 2.5 and pulled away at speed 0.01. The height $h$ at which the plank touches the wall is given by $\sqrt{ 36 - u^2}$. The question is, at what speed does the plank hit the floor. So I used the chain rule to obtain that $h'(t) = \frac{-1}{2h} \cdot 0.01 \cdot 2u$. Now when the plank hits the floor, $h=0$, the speed at this time is undefined. This is supposed to be an easy exercise in the chain rule but I cannot figure out where I went wrong.

It is correct that the point of contact with the wall is moving down infinitely fast when the plank hits the floor. You can think of the base being fixed and the wall moving away from the base. The infinite speed comes because when the wall hits the floor, the plank is perpendicular to the wall, so the angle of the plank is not constrained.