What mistake did I make when solving for the equilibrium of a rigid object?

[agusb1]

Homework Statement

A vaulter holds a 29.4 N pole in equilibrium by exerting an upward force with her leading hand and a downward force with her trailing hand as shown in Figure (included below). Point C is the center of gravity of the pole.

Relevant Equations

Sum of forces in y direction = -D + U - Fg = 0

Here's the task:

My attempt at a solution (I choose C as an axis):

However, the textbook solution says D should be 58.8. What am I doing wrong?

 

[Orodruin]

First of all, please remove the vector arrows over your forces. Although the forces are vectors, what you are actually using in your computations is their magnitudes.

Second, the above tends to confuse you when you are writing down the torque equation. Be mindful of the proper directions of the torques.

Third, while not wrong, choosing C as the point for considering the torque is not ideal. A good choice would let you disregard one of your unknowns completely for that equation rather than having the known gravitational force provide no torque.

 

[agusb1]

I see. I realize I had incorrectly assumed D and U had the same direction, but they have opposite ones. I also had incorrectly written -29.4 in the torque equation when it should had been +29.4. I re-calculated it and now I get the correct result. Thanks.