Force and Acceleration

Question

An engineer proposes a new roller coaster for daredevil teens and adults. Along with sizzling vertical loops and horizontal curves, her track would travel beneath a waterfall and into a dark tunnel plunging 10 m to the finish. If the engineer designs her roller coaster to travel a maximum of 30 m/s, approximately how high must the first hill be?

 

SHOW ALL WORK PLEASE.

 

May use if needed: 

 

Fc = Fn + Fg

 

Fc = MAc

 

Ac = v^2/r

Answer 1

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