#### Answer

$h=1.57m$

#### Work Step by Step

The required height can be determined as follows:
We know that:
$e=\frac{v_{g2}-v_{By}^{\prime}}{v_{By}-v_{g1}}$
We plug in the known values to obtain:
$0.8=\frac{0-v_{By}^{\prime}}{-6.946-0}$
This simplifies to:
$v_{By}^{\prime}=5.556m/s\uparrow$
From the equation of kinematics
$v_{Cy}^2=v_{By}^{\prime 2}+2a_c(S_{Cy}-S_{By})$
We plug in the known values to obtain:
$0=(5.556)^2+2(-9.81)h$
This simplifies to:
$h=1.57m$