Kinematics question

Yegor

Disc (R=5m) is rotating in horizontal plane (period T=10 s). Archer and target are located on the same diameter directly opposite each other (Distance between them equals 10m). Archer shoots. Bullets speed v=300m/s. I have to define angle alpha (approx) at which archer have to aim at target. We can assume that $$\omega R << v$$.
I want to solve this in 1) inertial and 2) rotating frame.
I did:
$$2R=vt$$
$$d=\omega R t$$ (d is length of arc)
$$\alpha =d/2R=\omega R/v=2\pi R/Tv$$
But the answer is $$4\pi R/Tv$$
What is wrong?
And i don't know how to make it in rotating frame.
I know that i have to take into account Koriolis and centripetal acceleration.
$$\vec{a_{rel}}=2\vec{v}_{rel}\times\vec{\omega}+(\omega)^2\vec{r}$$
Help me please make a step further. Thank you

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