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° north latitude is about 3429.5 miles. Therefore, a location on Earth at 30° north latitude is spinning on a circle of radius of 3429.5 miles. Compute the linear speed on the surface of Earth at 30° north latitude.

Short Answer

Expert verified

The linear speed on the surface of the earth at $30 °$ 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° north latitude is about 3429.5 miles. Therefore, a location on Earth at 30° 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,

$1 ° = \frac{24 hours}{360 °}$

Now, check for 30 degrees.

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

Convert the angle 30 degrees into radian.

$\begin{array}{rcl} θ & = & 30 ° \times \frac{π}{180 °} \\ = & \frac{π}{6} \end{array}$

Step 3. Find the linear speed.

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

$v = \frac{θ}{t} \cdot r$

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

$\begin{array}{rcl} v & = & \frac{\frac{π}{6}}{2} \cdot 3429.5 \\ = & \frac{π}{12} \cdot 3429.5 \\ = & \frac{\frac{22}{7}}{12} \cdot 3429.5 \\ \approx & 898 miles / hours \end{array}$

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Short Answer

Step by step solution

Step 1. Given information.

Step 2. Explanation to find the value.

Step 3. Find the linear speed.

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