Answer
The vertical component of the force on the bar from the hinge is $~~250~N$
Work Step by Step
We can let "up" be the positive direction.
To find the vertical component of the force on the bar from the hinge $F_{hy}$, we can consider the net vertical force on the bar:
$\sum F_y = 0$
$F_{hy} + (500~N)~sin~30.0^{\circ}-200~N-300~N = 0$
$F_{hy} = 200~N+300~N - (500~N)~sin~30.0^{\circ}$
$F_{hy} = 250~N$
The vertical component of the force on the bar from the hinge is $~~250~N$.
