Speed of light of a falling ladder

Question

The classic problem of a ladder that is leaning on a wall, if a ladder starts to fall down by sliding against the wall, will the top of the ladder ever reach the speed of light? I am confused about this topic. The triangle is assumed to be a right triangle. My professor asked the class this question and I cannot intuitively solve it. I understand that this "should" occur when

$$x (\text{ distance from the wall }) = L \text{ length of ladder} $$

Which then the rate at which the top of the ladder is falling "should" be infinity. Obviously this is incorrect.

Answer 1

@Hawaiian Rolls Your problem is stated differently from here:

"The classic problem of a ladder that is leaning on a wall, if a ladder starts to fall down by sliding against the wall, will the top of the ladder ever reach the speed of light?"

I don't think your professor said "sliding against the wall" the whole time because it would be incorrect.

Your version of the problem does not state clearly if the ladder is required to always stay in contact with the wall while sliding down.

If it is required, the velocities in the horizontal direction and the vertical direction are constrained by a relationship involving gravitation. In this case, there is no way you can have a constant horizontal speed at all.

In the other problem that Toby Mak mentioned, the constant horizontal speed will cause the ladder to pull off away from the wall immediately.

In fact, at time $t = 0$, the horizontal speed is already greater than the vertical speed. Thus, immediately after $t=0$, the horizontal speed will pull the ladder away from the wall.

Answer 2

This website here gives a good explanation on why the falling ladder does not fall at an infinite speed. Hint: the triangle is only assumed to be a right triangle — it might not be in all cases.