Answer
$h=23.75m$, $v_C=21.6m/s$
Work Step by Step
We can determine the required height and speed as follows:
We apply the equation of conservation of energy between A and B
$\frac{1}{2}m_A^2+mgh_A=\frac{1}{2}mv_B^2+mgh_B$
We plug in the known values to obtain:
$0+9.81h=\frac{1}{2}(8.578)^2+(9.81)(20)$
This simplifies to:
$h=23.75m$
Now, we apply the equation of conservation of energy between B and C to determine the speed
$\frac{1}{2}mv_B^2+mgh_B=\frac{1}{2}mv_C^2+mgh_C$
We plug in the known value to obtain:
$\frac{1}{2}(8.578)^2+(9.81)(20)=\frac{1}{2}v_C^2+0$
This simplifies to:
$v_C=21.6m/s$