Conservation of Energy

Question

If a roller coaster begins at rest at the top of a 26 meter hill, then at the bottom of the hill how fast will it be going?

Answer 1

Let m and v be the mass and speed, respectively, of the coaster. By conservation of energy, the gain in kinetic energy as the coaster reaches the bottom is equal to the potential energy lost: mv²/2 = 26mg. Dividing the equation by m and multiplying by 2, v² = 52g. Taking the square root on both sides, v = √(52g) = 23 m/s.