A 2000kg coaster is released 40 meters above the ground on a frictionless track. What is the approximate speed at ground level?

At the top, the coaster's gravitational potential energy is

(mass) x (gravity) x (height) =

(2,000kg) x (9.8m/s²) x (40m) = 784,000 joules.

If the track is frictionless, then its speed at the bottom is the same

as if it were simply dropped. At ground level, ALL of its potential

energy has changed into kinetic energy.

Kinetic energy = (1/2) x (mass) x (speed) ²

We know how much potential energy it had before it dropped,

and all of that energy is kinetic at the borrom:

784,000 joules = (1/2) (2,000kg) x (speed) ²

Divide each side by 1,000: 784 = (speed) ²

Speed = √784 = 28 meters per second

(That's about 62.6 miles per hour.)