Answer
$79.4m$
Work Step by Step
We can find the required radius as follows:
$\Sigma F_x=Nsin\theta=ma_c=\frac{mv^2}{r}$
$\implies r=\frac{mv^2}{Nsin\theta}$.......eq(1)
Similarly $\Sigma F_y=Ncos\theta -mg=0$
$\implies N=\frac{mg}{cos\theta}$
We plug in value of $N$ in eq(1) to obtain:
$r=\frac{mv^2 cos\theta}{mg sin\theta}$
$\implies r=\frac{v^2}{gtan\theta}$
We plug in the known values to obtain:
$r=\frac{(22.7)^2}{(9.81)tan33.5^{\circ}}$
$r=79.4m$
