Arturo O. answered • 05/26/16

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Assuming the roller coaster drops from rest at a height h and attains a speed v at the bottom of the fall, then

mgh = (1/2) mv^2

The mass cancels out, so

gh = v^2 / 2

h = v^2 / (2g) = (30 m/s)^2 / (2 * 9.8 m/s^2) = 45.92 m

Assuming the final 10 m plunge is included in h, then subtract the 10 m to get h' = 35.92 m