1. Because the force is vertical the only component of the motion that matters is the change in height -- from a height of one meter to a height of 8 meters. The person does 823.20 newton-meters work and gravity does -823.20 newton-meters work.

  2. The total force has two components. First, the force due to gravity is (0, 0, -49) newtons. Second the force due to the wind is

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    Notice that this vector points from the northeast toward the southwest and has magnitude 2. The total force including both the force due to wind and the force due to gravity is

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    and taking the dot product of the total force with the motion (2, 0, 4) we get

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    This is the work done by the wind and gravity. The work done by a person moving the object against the wind and gravity would be

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Copyright c 1997 by Frank Wattenberg, Department of Mathematics, Montana State University, Bozeman, MT 59717