Question

A roller coaster glides from rest from the top of an 80.0 meter hill. What is the speed of the roller coaster at the bottom of the hill?

Answer 1

So this is the case of energy conversion. From potential to kinetic.
As energy is conserve:
Epi+Eki=Epf+Ekf ; i for initial and f for final. At begining object at rest hence Eki=0 while at final, object on the lowest position, hence epf=0 therefore:
Epi=Ekf
M.g.h=1/2.m.v^2
Assume no mass change during the process, then
G.h=1/2.v^2
Hence v at bottom:
v=sqrt(2×g×h) assume g=10m/s^2
=sqrt(2×10×80)=sqrt(1600)=40m/s
Hence velocity in the bottom is 40 m/s