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Winter Wonderland

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Rochester winters are famous for their snow, and the next one isn’t far off. The more the merrier I say, except when it's that really dense, slushy snow that clogs up your driveway. Unless of course, you're using it to peg some random stranger with. But what if it breaks up like mine always do? Will it still hit the mark?


Let's say we have a nice big snowball, separated into three chunks. The dense center has a mass of .02 kg. The next, slightly less dense section has .01 kg, and the outer ring is fluffy snow with .005 kg, for a total of .035 kg. It's thrown from a teenage boy's arm height - let's say 1.2 m - at a small child's head - about .5 m high. The child is 6 m away. The snowball is thrown at exactly 15.88 m/s horizontally so that it may hit the target perfectly. But, after 2 m, .005 kg breaks off, and after another 2m, .01 kg breaks off too. Using conservation of momentum, knowing each piece breaks off at the current speed of the snowball, we find the speed in the x-plane to be 15.88 m/s again! Repeating the same procedure for the next 2 m, we again find that the speed of the snowball hasn’t changed. Thus, the snowball hits its target perfectly, and the scientists involved get a stern talking to from an angry mother. Complete success!

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