Chapter 10.1, Problem 41E

To determine

Find the magnitude of the given force.

Answer to Problem 41E

The central angle is ${55}^{°}$ .

Explanation of Solution

Given:

The given force (expressed by the vector) is $\langle 115,2018,0\rangle$ .

Calculation:

Use formula $A=\frac{\theta }{360}\cdot 2\pi r$ , where

  $A=$ arc length

  $\theta =$ central angle

  $r=$ radius of the circle

Draw a diagram for the given problem.

  

In the given problem

  $A=11.5"$ arc length

  $r=12"$

Now,

  $\begin{array}{l}A=\frac{\theta }{360}\cdot 2\pi r\\ 11.5=\frac{\theta }{360}\cdot 2\pi \cdot 12\\ \Rightarrow 11.5=\frac{\theta }{24\cdot 15}\cdot 24\pi \\ \Rightarrow 11.5=\frac{\theta }{15}\cdot \pi \\ \Rightarrow 11.5\cdot 15=\frac{\theta }{15}\cdot \pi \cdot 15\\ \Rightarrow 11.5\cdot 15=\theta \cdot \pi \\ \Rightarrow \frac{11.5\cdot 15}{\pi }=\frac{\theta \cdot \pi }{\pi }\\ \Rightarrow \frac{11.5\cdot 15}{3.14}=\theta \\ \Rightarrow 54.9=\theta \\ \Rightarrow \theta \approx {55}^{°}\end{array}$

Hence the central angle is ${55}^{°}$ .