What expression represents the speed of a roller coaster if it drops from height of 200 feet?

To find the speed of a roller coaster dropping from a height of 200 feet, we can use the principle of conservation of energy. The potential energy at the top (PE = mgh) converts to kinetic energy (KE = 0.5mv²) at the bottom. Ignoring air resistance and friction, the speed can be calculated using the formula ( v = \sqrt{2gh} ), where ( g ) is the acceleration due to gravity (approximately 32.2 ft/s²). Thus, the speed at the bottom would be ( v = \sqrt{2 \times 32.2 , \text{ft/s}^2 \times 200 , \text{ft}} ).