Answer
$8.46 \ m/s$
Work Step by Step
We know the y-forces must cancel, for the ball remains in the horizontal plane. Thus, we find:
$mg = F_t sin12$
We also know that the x-component of tension is the centripetal force:
$F_tcos12 =\frac{mv^2}{r}$
Thus, we use substitution to find:
$mg/tan12=\frac{mv^2}{r}$
$v=\sqrt{grtan12}=\sqrt{\frac{9.81\times1.55}{tan12}}=8.46 \ m/s$
