A 500 kilogram roller coaster starts from rest at the top of an 80 meter hill. What was its speed at the bottom at the hill?

m = mass of the roller coaster = 500 kg

h = height of the hill = 80 m

v = speed of the roller coaster at the bottom of the hill = ?

using conservation of energy

kinetic energy at the bottom of the hill = potential energy at the top of hill

(0.5) m v² = m g h

(0.5) v² = g h

inserting the values

(0.5) v² = (9.8) (80)

v = 39.6 m/s

hence the speed at the bottom comes out to be 39.6 m/s