. [20 points] In questions (a) and (b) show all your calculations and units as applicable. You will be assessed both on your answers and your explanations of how you got them. (a) Hurricanes are powered by heat energy in the atmosphere and the ocean. Typically, a "small" hurricane uses an amount of heat roughly equal to Y thousand atomic bombs. If just half of the excess heat built up in Earth's atmosphere since the year 1900 went into producing hurricanes, about how many more hurricanes might we expect in the world every year? (b) Compute the gravitational potential energy of a water bottle - you choose its size - that is lifted X centimeters into the air near the surface of the Earth. Then compute how much kinetic energy is released if the water bottle is dropped and it falls four meters. Give your answers in units of joules