Answer
$F=367.3N$
Work Step by Step
The required force can be determined as follows:
$\Sigma U_{A\rightarrow B}=F(AC-BC)$
$\Sigma U_{A\rightarrow B}=F(\sqrt{(8)^2+(6)^2})=F(3.675)$
Now according to the principle of work and energy
$\frac{1}{2}+\Sigma U_{A\rightarrow B}=\frac{1}{2}mv_B^2$
We plug in the known values to obtain:
$0+F(3.675)=\frac{1}{2}(75)(6)^2$
This simplifies to:
$F=367.3N$
