Two water-slide riders, A and B, start from rest at the same time and same height, h but on differently shaped slides. Required:
a. Which rider is traveling faster at the bottom?
b. Which rider makes it to the bottom first? Ignore friction and assume both slides have the same path length.

a. None

b. Both

Explanation:

a. Which rider is traveling faster at the bottom?

Since both riders fall from the same height, h, their potential energy, U at the top equals their kinetic energy, K at the bottom.

U = mgh and K = 1/2mv²

Since U is he same for both water-slide riders, then K will be the same and thus their speed at the bottom will be the same. This is shown below.

K = U

1/2mv² = mgh

v² = 2gh

v =√(2gh) where v = speed of rider at the bottom, g = acceleration due to gravity and h = height of slide.

Since the height is the same, so their speed at the bottom is the same. So, none of the riders travels faster than the other since they have the same speed at the bottom.

b. Which rider makes it to the bottom first? Ignore friction and assume both slides have the same path length.

Since the path length of the water slides are the same and friction is neglected, both water-slide rider get to the bottom at the same time since the distance moved is the same and they both start from rest.

So, both riders make it to the bottom at the same time.