Question

A palm tree weighing 1000 lb. is inclined at an angle of 60° (see figure below). The

weight of the tree may be resolved into two resultant forces, a force P1 = 900 lb.
acting at a point 12 ft from the base and a force P2 = 100 lb. acting at the top of the
tree, which is 30 ft long. Assume yourself at 2/3rd from the base and exerting a
downward force of P3 = 132lb due to self-weight. The diameter
at the base of the tree is 14 in.
At what angle is the palm tree inclined?
a) 30°
b) 45°
c) 60°
d) 90°

Answer 1

The palm tree is inclined at an angle of approximately 84.26°, which is not provided as an option in the given choices.

Step-by-step explanation:

To find the angle at which the palm tree is inclined, we can calculate the vertical and horizontal components of the resultant forces. The weight of the tree, 1000 lb., can be resolved into two forces: P1 = 900 lb. acting 12 ft from the base and P2 = 100 lb. acting at the top of the tree. We can use trigonometry to find the angle:

tan(θ) = horizontal component / vertical component

tan(θ) = 900 lb. / 100 lb.

tan(θ) = 9

θ = arctan(9) ≈ 84.26°

The palm tree is inclined at an angle of approximately 84.26°. None of the options given (a, b, c, d) match this result, so the correct angle is not provided as an option.