Final answer:
The kinetic energy of the coaster full of people with a mass of 1200 kg traveling at 16 m/s down the first hill is calculated using KE = (1/2)mv², which results in a kinetic energy of 153,600 joules.
Step-by-step explanation:
When you are visiting Six Flags Over Texas and riding the latest rollercoaster, the coaster full of people with a mass of 1200 kg traveling at 16 m/s down the first hill possesses kinetic energy (KE). The kinetic energy, given no energy is lost due to factors like air resistance or friction, can be calculated using the equation KE = (1/2)mv², where m is the mass and v is the velocity. Inserting the values given in the problem, the equation becomes KE = (1/2) × 1200 kg × (16 m/s)². Calculating this, we find the kinetic energy to be KE = (1/2) × 1200 kg × 256 m²/s² = 153,600 kg·m²/s². Therefore, the rollercoaster has a kinetic energy of 153,600 joules as it travels down the first hill. As the rollercoaster descends the first hill at 16 m/s, its kinetic energy (KE) can be calculated using the formula KE = 0.5 * mass * velocity^2. Plugging in the values, we get KE = 0.5 * 1200 kg * (16 m/s)^2. First, square the velocity: 16 m/s * 16 m/s = 256 m^2/s^2. Then, multiply by half the mass (0.5 * 1200 kg = 600 kg). The result is KE = 600 kg * 256 m^2/s^2 = 153,600 J (joules). Therefore, the rollercoaster has 153,600 joules of kinetic energy as it speeds down the first hill at Six Flags Over Texas.