= Solution
Take the initial thrower and receiver positions to be $(-a,0)$ and $(a,0)$, with counterclockwise <angular velocity> $\omega$. Interpret $v$ as the launch <speed> relative to the thrower. The ball inherits the thrower's tangential <velocity>, so in an <inertial frame> its initial horizontal <velocity> is $(v,-a\omega)$. The flight time across the diameter is $t_f\simeq2a/v$. During that time the receiver moves approximately $+a\omega t_f$ sideways while the ball moves $-a\omega t_f$. Thus the <transverse miss on a rotating platform> is
$$
\boxed{d\simeq2a\omega t_f=\frac{4a^2\omega}{v}.}
$$
The ball passes behind the receiver in the sense of rotation. Equivalently, in the rotating frame its transverse <Coriolis acceleration> has magnitude $2\omega v$ to leading order; integrating over $t_f$ gives $d=\tfrac12(2\omega v)t_f^2$. Terms neglected here are higher order in $a\omega/v$. Specifying an initially radial launch <velocity> in the inertial frame instead would define a different throw and would lose the inherited tangential <velocity>.
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