A guy wire $78$ feet long runs from the top of a pole $56$ feet high to the ground and pulls on the pole with a force of $290$ pounds. What is the horizontal Pull on the top of the poll?
I am not sure how do this problem. I tried to draw a triangle and one side is $56$ and the hypotenuse is $78$, but I am not sure what to do.
On
So, force is a vector and any force vector can be visualized in the Cartesian coordinate plane and decompose this vector into its components (horizontal, vertical, etc.).
Always drawing a diagram (Force diagram) in these word problems is very helpful. So, draw a right triangle that best depicts the scenario.
We want to find the angles of this triangle that will help us answer this question. What is this angle? Let's say we want to find the angle $(\theta)$ between the height $(56)$ and the hypotenuse $(78)$. $\cos(\theta)=56/78$
Now, we have that the person is pulling the wire so that the force on the wire is along the wire. Given the $\theta$ that we defined, the magnitude of the vertical component of the force is the magnitude of the resultant force $\cdot \cos(\theta)$ and the horizontal component of the force is the magnitude of the resultant force $\cdot\sin(\theta)$.
I will leave the specific calculations up to you. Cheers,
Consider the force diagram:
Observe that the horizontal component of the force is $\boldsymbol{F}_h = \boldsymbol{F}\cos\theta$, where $\boldsymbol{F} = 2900~\text{lb}$ in the indicated direction. Also, observe that $$\theta = \arcsin\left(\frac{56~\text{ft}}{78~\text{ft}}\right)$$