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 $$x$$ 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.
×