The roof of an apartment building is 58 meters high. A water tank on the roof has a mass of 38,000 kilograms. What is the potential energy of the water tank? (1 point) \( 211,672,160 \mathrm{~J} \) O \( 21,599,200 \mathrm{~J} \) \( 2,204,000 \mathrm{~J} \) O \( 10,799,600 \mathrm{~J} \)

To find the potential energy (PE) of the water tank, you can use the formula: \[ PE = mgh \] where \( m \) is the mass (in kilograms), \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \mathrm{m/s^2} \)), and \( h \) is the height (in meters). Given: - Mass \( m = 38,000 \, \mathrm{kg} \) - Height \( h = 58 \, \mathrm{m} \) - \( g \approx 9.81 \, \mathrm{m/s^2} \) Plugging in the values gives: \[ PE = 38,000 \, \mathrm{kg} \times 9.81 \, \mathrm{m/s^2} \times 58 \, \mathrm{m} \approx 21,599,200 \, \mathrm{J} \] So the correct answer is \( 21,599,200 \mathrm{~J} \). Potential energy calculations are essential not only in physics but also in real-world scenarios such as designing buildings and ensuring safety. Understanding how energy is stored due to height helps engineers make informed choices when it comes to structural integrity and load-bearing capacities. It’s not just numbers; it’s about keeping people safe and secure! For those curious about diving deeper, consider exploring concepts like gravitational potential energy in different environments. You can also examine how varying heights affect energy storage in everything from hydroelectric dams to roller coasters. If you’re hooked, check out introductory physics textbooks or fun science experiment guides that demonstrate these principles in action!