This problem was asked to a friend of mine in the KVPY interview. He was asked to describe the motion qualitatively. I wanted to analyze it quantitatively.

A solid wooden sphere with density less than water is released with a speed v in water, along the positive $x$ axis, at the origin.

Find its maximum $x$ coordinate (in meters)

**Details and assumptions**

- Stoke's law is applicable.
- The tank is very wide and very deep, so that the sphere loses all horizontal velocity before breaching the surface.
- Mass of the sphere = $\SI{6}{\kilo\gram}$.
- Initial speed = $\SI{\pi}{\meter/\second}$.
- Radius of sphere = $\SI{0.5}{\meter}$.
- Coefficient of viscosity = 1.

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