Hail is produced in severe thunderstorms when an updraft draws moist surface air into subfreezing air above 10,000 feet. The speed of the updraft s, in mph, affects the diameter of hail (in inches). According to National Weather Service data, the rate of change of hail size with respect to updraft speed dh / ds = 0.001144s0.922 is inches of diameter per mph of updraft.
(a) When updraft speeds approach 60 mph, hail is golf-ball-sized. Use h = 1.5 and s = 60 to find a model for h(s).
(b) Use the model to find the hail size for an updraft speed of 100 mph.