review the diagram. a pair of tow trucks are pulling on a trailer that is stuck in mud. the first truck…

review the diagram. a pair of tow trucks are pulling on a trailer that is stuck in mud. the first truck pulls with a force of 10,000 pounds at a 110° angle from the second truck, which is pulling with a force of 7,500 pounds. what is the magnitude of the resultant force? 9,821 pounds 10,244 pounds 14,405 pounds 24,226 pounds

review the diagram. a pair of tow trucks are pulling on a trailer that is stuck in mud. the first truck pulls with a force of 10,000 pounds at a 110° angle from the second truck, which is pulling with a force of 7,500 pounds. what is the magnitude of the resultant force? 9,821 pounds 10,244 pounds 14,405 pounds 24,226 pounds

Answer

Explanation:

Step1: Recall the law of cosines for vectors

If we have two - vectors $\vec{F}_1$ and $\vec{F}_2$ with an angle $\theta$ between them, the magnitude of the resultant vector $\vec{R}$ is given by $R=\sqrt{F_1^{2}+F_2^{2}+2F_1F_2\cos\theta}$. Here, $F_1 = 10000$, $F_2=7500$, and $\theta = 110^{\circ}$, and $\cos(110^{\circ})\approx - 0.342$.

Step2: Substitute the values into the formula

[ \begin{align*} R&=\sqrt{(10000)^{2}+(7500)^{2}+2\times10000\times7500\times\cos(110^{\circ})}\ &=\sqrt{100000000 + 56250000+150000000\times(- 0.342)}\ &=\sqrt{100000000 + 56250000-51300000}\ &=\sqrt{104950000}\ &\approx10244 \end{align*} ]

Answer:

10,244 pounds