Answer
$v=8.48m/s$
Work Step by Step
In the horizontal case, only the tension in the string provides the centripetal force in all positions. Therefore, the tension is constant and equals $$T_h=F_c$$
In the vertical case, the tension $T_v$ changes according to the position of the stone. $T_v$ is maximum at the bottom position, since it has to oppose the stone's weight to provide $F_c$. Therefore, $$T_v^{max}=F_c+mg$$
Since $T_v^{max}=1.15T_h$, we have $$F_c+mg=1.15F_c$$ $$mg=0.15F_c=0.15\frac{mv^2}{r}$$ $$g=\frac{0.15v^2}{r}$$ $$v=\sqrt{\frac{gr}{0.15}}$$
We know that $g=9.8m/s^2$ and $r=1.1m$. Therefore, $$v=8.48m/s$$
