How can a sail boat achieve speeds faster than the velocity of the wind?

When going at an angle to the wind, sails work with the combination of the true (natural) wind and the wind that your forward motion creates. This is called apparent wind, and is a greater force than just the true wind alone.

The reason that sailing to an angle is important is that sails are foils. Like an airplane wing, they create a vacuum that creates lift and sucks the boat forward (unless the wind is at your back, which is actually the slowest way to sail). The larger the sail area, the larger a vacuum you create, and the faster you can go.

(Also, if you're curious, the reason you can't sail directly into the wind is because it makes the sail flap like a flag. This destroys the curved shape in the sail, which is what makes it a foil and what creates the forward motion)

The sail on a sailboat or ice boat does not catch the wind, and carry the boat before the wind. Instead, the sail is an airfoil, just like the wings on an airplane. It generates lift the same way as a wing does. The only difference is that the direction of the lift is horizontal, not vertical. And the amount of lift generated depends on the speed of the wind and the surface area of the sail. So a large sail on a small light ice boat can produce enough forward speed that the boat can go much faster than the wind speed that day.

Yes, if you are sailing directly away from the wind, you can't go faster than the wind. But on a broad reach, at about right angle to the wind, the wind exerts a constant force on the sail, which is set to about 45 degrees to the wind. The constant force will cause a continued acceleration until friction limits it.

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you cant when sailign in the same direction the wind is blowing...

but you can when sailing at an angle to the wind.... its all to do with relative vectors.

Head for the nearest waterfall :)