Viscous Trajectory

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 xx axis, at the origin.

Find its maximum xx 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 = 6 kg\SI{6}{\kilo\gram}.
  • Initial speed = π m/s\SI{\pi}{\meter/\second}.
  • Radius of sphere = 0.5 m\SI{0.5}{\meter}.
  • Coefficient of viscosity = 1.

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