I am confused by this answer. How can in part b Kathleen get to the bottom first

Question

I am confused by this answer. How can in part b Kathleen get to the bottom first if they've stayed they will finish at the same speed and distance of the path is same ? Please help anyone thanks

EXAMPLE 5 Speeds on two water slides. Two water slides at a pool are shaped differently, but start at the same height h (Fig. 9). Two riders, Paul and kathleen, start from rest at the same time on different slides. (a) Which rider. aul or Kathleen, is traveling faster at the bottom? (b) Which rider makes it to the CONCEPTUAL pool are s and Kathleen, star bottom first? Ignore frict ttom first? Ignore friction and assume both slides have the same path length. RESPONSE (a) Each rider's initial potential energy mgh gets transformed to kinetic d u at the bottom is obtained from, 2mv2 = migh. The mass cancels and so the speed will be the same, regardless of the mass of the rider. Since they descend the same vertical height, they will finish with the same speed. (b) Note that Kathleen is consistently at a lower elevation than Paul at any instant, until the end. This means she has converted her potential energy to kinetic energy earlier. Consequently, she is traveling faster than Paul for the whole trip, and because the energy, so the speed v at the bottom is obtained from 2nm distance is the same, Kathleen gets to the bottom first.

Explanation / Answer

here Paul, Kathleen are started at same time having sam path as the conversion of energy from gravtaional potential energy to kinetic energy

mgh = 1/2 mv^2 ==> v= sqrt(2gh)

given that kathleen is at lower elevation so the acceleration due to gravity will be more than paul at higher elevation ,

we know that acceleration due to gravity will decrease as we move at heigher levels .

if g is more consequently Kathleen will reach first than Paul because same path length.

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