The cable AO exerts a force on the top of the pole of F = {—120i — 90j — 80k} lb. If the cable has a length of 34 ft, determine the height z of the pole and the location (x,y) of its base.

The cable AO exerts a force on the top of the pole of F = {—120i — 90j — 80k} lb. If the cable has a length of 34 ft, determine the height z of the pole and the location (x,y) of its base.

Solution

 Here the force f has its value along x, y, z directions are 120, 90, 80.

So the resultant force is equal to 170.

So the angles are along x, y, z cos inverse of
(9120/170),(90/170),(80/170).

Now the length of the cable is 34.
So the components along,

x axis 34*(120/170) = 24.
y axis 34*(90/170) = 18.
z axis 34*(80/170) = 16.