Answer
$h=39.3m$, $\rho=26.2m$
Work Step by Step
We can determine the required height and the minimum radius of curvature as follows:
$\frac{1}{2}mv_1^2+mgh=\frac{1}{2}mv_2^2$
We plug in the known values to obtain:
$\frac{1}{2}(0)^2+9.81h=\frac{1}{2}(\frac{100\times 1000}{3600})^2$
This simplifies to:
$\implies h=39.3m$
Now $\Sigma F_n=ma_n$
$\implies 39.24m-mg=m\frac{v^2}{\rho}$
We plug in the known values to obtain:
$39.24-9.81=\frac{(\frac{100\times 1000}{3600})^2}{\rho}$
This simplifies to:
$\rho=26.2m$
