Determine the distances h1 and h2, and the maximum tension in the cable

Draw the free body diagram of the cable
Sum of the horizontal forces is zero
0
0
x
A B
A B
F
H H
H H

 



Sum of the vertical forces is zero
0
0
3 0
......(1)
y
A B
A B
F
V V W W W
V V W

    
  

A BV + V = 3W
Taking moment about A
       
0
2 5 9 14 14
2 5 9 14 14
16 14 14
8 7 7 ......(2)
A
B B
B B
B B
B B
M
W W W H V
W W W H V
W H V
W H V

        
   
 
 


Taking moment about B
         
0
5 9 12 14 14 0
5 9 12 14 14
13 7 7 ......(3)
B
A A
A A
A A
M
W W W H V
W W W H V
W H...