Q. 103 Linear Speed on Earth Earth rota... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 6: Q. 103 (page 366)

Linear Speed on Earth Earth rotates on an axis through its poles. The distance from the axis to a location on Earth 30掳 north latitude is about 3429.5 miles. Therefore, a location on Earth at 30掳 north latitude is spinning on a circle of radius of 3429.5 miles. Compute the linear speed on the surface of Earth at 30掳 north latitude.

Short Answer

Expert verified

The linear speed on the surface of the earth at $30 掳$ the north latitude is $898 \frac{miles}{hour}$

Step by step solution

Step 1. Given information.

Consider the given information,

The distance from the axis to a location on Earth at 30掳 north latitude is about 3429.5 miles. Therefore, a location on Earth at 30掳 north latitude is spinning on a circle of radius of 3429.5 miles.

Step 2. Explanation to find the value.

Since-, the earth rotates 360 degrees in 24 hours. Thus,

$1 掳 = \frac{24 hours}{360 掳}$

Now, check for 30 degrees.

$\begin{array}{rcl} t & = & \frac{24 hours}{360 掳} 脳 30 掳 \\ = & \frac{24 hours}{12} \\ = & 2 hours \end{array}$

Convert the angle 30 degrees into radian.

$\begin{array}{rcl} 胃 & = & 30 掳脳 \frac{蟺}{180 掳} \\ = & \frac{蟺}{6} \end{array}$

Step 3. Find the linear speed.

Since angular speed is $蝇 = \frac{胃}{t}$ and linear speed is $v = r 蝇$ . Thus,

$v = \frac{胃}{t} 路 r$

Substitute the angle $\frac{蟺}{6}$ , time is 2 hours and the radius is $3429.5$ . Substitute the values in the formula,

$\begin{array}{rcl} v & = & \frac{\frac{蟺}{6}}{2} 路 3429.5 \\ = & \frac{蟺}{12} 路 3429.5 \\ = & \frac{\frac{22}{7}}{12} 路 3429.5 \\ 鈮� & 898 miles / hours \end{array}$