Answer
The vertical component of the force on the rod from the wall is directed upward.
Work Step by Step
In part (a), we found that the tension in the cable is $~~T = 408.5~N$ and the angle of the cable is $\theta = 53.1^{\circ}$
We can let "up" be the positive direction.
To find the vertical component of the force on the rod from the wall $F_{wy}$, we can consider the net vertical force on the rod:
$\sum F_y = 0$
$F_{wy} + T~sin~\theta - (50.0~kg)(9.8~m/s^2) = 0$
$F_{wy} = (50.0~kg)(9.8~m/s^2)- T~sin~\theta$
$F_{wy} = (50.0~kg)(9.8~m/s^2)- (408.5~N)~sin~53.1^{\circ}$
$F_{wy} = 163~N$
Since the vertical component of the force on the rod from the wall is positive, the vertical component of the force on the rod from the wall is directed upward.
