[Q] The horizontal displacement $\Delta$ of the trajectory of a spinning ball depends on the mass $m$ and diameter $d$ of the ball, the air density $\rho$ and viscosity $\mu$, the ball's rotation rate $\omega$, the ball's speed $U$, and the distance $L$ traveled.
(a) Use dimensional analysis to predict how $\Delta$ can depend on the other parameters.

(b) Simplify your result from part (a) for negligible viscous forces.

(c) It is experimentally observed that $\Delta$ for a spinning sphere becomes essentially independent of the rotation rate once the surface rotation speed, $\omega d/2$, exceeds twice $U$. Simplify your result from part (b) for this high-spin regime.

(d) Based on the result in part (c), how does $\Delta$ depend on $U$?

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