Does angle of inclination between slide and the floor affect speed at the bottom? [closed]

I obtain the following question in this link.

I don't understand why the velocity at the bottom for the four slides are the same. I thought the velocity depends on the angle of inclination between slide and the floor. In other words, my answer is

$$v_D > v_A > v_B > v_C$$

Can anyone explain to me why all speeds are the same?

• VtC voters: check the link, it is not homework. Commented Aug 4, 2016 at 4:00
• @peterh : You misunderstand the definition of "homework" on this site. Full title is "homework and exercises," which includes all questions of a "homework-like" nature, even if done for self-study. See meta.physics.stackexchange.com/questions/714 Commented Aug 4, 2016 at 9:45
• @sammygerbil You are right. Although I think, maybe the homework (& exercises) policy could be softened on pragmatical reasons, ref1, ref2. Commented Aug 4, 2016 at 15:57
• @peterh : I agree, the policy should be revised, although I think it should not depend on whether the question has actually been set for homework - that would be too difficult to verify. I agree this question should be on topic. But according to the official policy I think it is not. If you want to change policy, get involved on the Physics Meta site. Commented Aug 4, 2016 at 16:19

First, the reason the child is moving at all is that the potential energy at the top is converted into kinetic energy at the bottom. If the initial height is $h$ and the mass of the child is $m$, we have a final speed $v$ of $$mgh=\frac{1}{2}mv^2\to v=\sqrt{2gh}$$ This is clearly independent of the path the child takes to get to the bottom, and so given that $h$ is the same in all cases, $v$ will also be the same. The child could be moving at a non-zero initial velocity, but this doesn't affect the result; the initial energy (and thus the final energy) will still be the same.