Answer
$h=3.12ft$
Work Step by Step
The required height can be determined as follows:
We know that
$\Sigma F_y=0$
$\implies N_A-W=0$
$\implies N_A=W$
$\implies N_A=W=4000lb$
We apply the equation of motion in x-direction
$\Sigma F_x=ma_{Gx}$
$\implies F_f=ma_G$
$\implies \mu_k N_A=\frac{W}{g}a_G$
We plug in the known values to obtain:
$0.8(4000)=\frac{4000}{32.2}a_G$
This simplifies to:
$a_G=25.76ft/s^2$
As $\Sigma M_A=\Sigma M_{kA}$
$\implies 2.5W=h ma_G$
$\implies 2.5(4000)=(\frac{4000}{32.2})(25.76)h$
This simplifies to:
$h=3.12ft$
