Dina has a mass of 50 kilograms and is waiting at the top of a ski slope that’s 5.0 meters high.

the maximum velocity she can reach when she skis to the bottom of the slope is meters/second.
use pe = m × g × h, g = 9.8 m/s2, and . ignore air resistance and friction.

All of Dina's potential energy Ep is converted into kinetic energy Ek so Ep=Ek, where Ep=m*g*h and Ek=(1/2)*m*v². m is the mass of Dina, h is the height of ski slope, g=9.8 m/s² and v is the maximal velocity. 

So we solve for v:

m*g*h=(1/2)*m*v², masses cancel out,

g*h=(1/2)*v², we multiply by 2,

2*g*h=v² and take the square root to get v

√(2*g*h)=v, we plug in the numbers and get:

v=9.9 m/s. 

So Dina's maximum velocity on the bottom of the ski slope is v=9.9 m/s.

the first american roller coaster was the mauch chunk switchback railway, built in the mountains of pennsylvania in the mid-1800s. the track, originally built to send coal to a railway, was reconfigured as a "scenic tour."

i think it's 35 meters