Answer
$$
t=1.32 \mathrm{~s}
$$
Work Step by Step
$$
\begin{array}{ll}
→+\quad & m v_{x 1}+\sum \int F_x d t=m v_{x 2} \\
& 5(3)+49.05 \sin 30^{\circ}(t)-25.487 t=5 v_G \\
↻+\quad & \left(H_G\right)_1+\sum \int M_G d t=\left(H_G\right)_2 \\
& -5(0.5)^2(8)+25.487(0.5)(t)=5(0.5)^2\left(\frac{v_G}{0.5}\right)
\end{array}
$$
Solving.
$$
\begin{aligned}
v_G & =2.75 \mathrm{~m} / \mathrm{s} \\
t & =1.32 \mathrm{~s}
\end{aligned}
$$
