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Ok.. This is how I tackled it:

First I converted 2.8 rev/s to rad/s using the equation 1 rev = 2*pi rad and got 17.593 rad/s

Then for the distance of a section of the wheel between the spokes I used the equation s = R*angle where R is the radius, so:

s = (0.38 m)((2*pi rad)/8) = 0.298 rad*m

Then I wasnt sure what I could do to get the minimum speed but I figured I'd find how long it'd take for s to "go by" using the angular velocity.. so I divided s by 17.593 and got 0.0170 seconds.. then I divided the length of the arrow (0.27 m) by 0.0170 seconds and got 15.88 m/s

Apparently that's not the answer. Anyone know whats up ?