A cylindrical glass of radius \(r=\sqrt{10}~cm\) and height \(h=20~cm\) is full of water. If the bottom half of the water suddenly disappears, the glass will jump up. Find the highest height above the ground that the bottom of the glass will rise **in cm**.

For your amusement and some nice physics background, you can look at this cartoon about the optimist, the pessimist, and the half-empty glass. Assume in this problem however, that the glass does NOT break.

**Details and assumptions**

To make the numbers easy, we can assume:

- The mass of the glass is \(m=0.1~kg\)
- The gravitational acceleration is \(-10~m/s^2\).
- The mass density of water is \(\rho=1000~kg/m^3\).
- The ambient pressure in the room is 100,000 Pa.
- Neglect any interaction between the water and the sides of the glass.

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