A motionless water skier sinks because the upward buoyancy force on the skier is less than the downward force of gravity on the skier.
A skier pulled by a boat does not sink into the water. Why?
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1Hint: how does an airplane fly? – Carl Witthoft Mar 21 '15 at 12:52
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Thanks. For posterity I'll include a link to the question What really allows airplanes to fly? – Scott Emmons Mar 22 '15 at 19:33
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The force that lifts the skier isn't buoyancy, it's the reaction force from the angled skis pushing water down. Water skiers start with their tips out of the water so that when the boat starts pulling, they can push against the water to lift themselves up. Once on top of the water, they still hold their skis at a slight angle, meaning the water they hit is pushed down (generating their wake). Thanks to Newton's third law, they themselves are pushed up by the same interaction.
There is a pretty accessible treatment of this at howstuffworks.com, complete with helpful diagrams.
morrna
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