Answer
$S=3.33ft$
Work Step by Step
According to the principle of work and energy
$T_A+\Sigma _{A-c}=T_C$
$\implies \frac{1}{2}m_A^2+U_w-U_f=\frac{1}{2}mv_2^2$
$\implies \frac{1}{2}+W(4)-\mu_kWS^{\prime}=\frac{1}{2}mv_2^2$
We plug in the known values to obtain:
$0-(30)(4)-(0.6)(30)S^{\prime}=0$
This simplifies to:
$S^{\prime}=6.667ft$
Now, $S=10-S^{\prime}$
$\implies S=10-6.667=3.33ft$
