Chapter 6: Q. 104 (page 366)

Linear Speed on Earth Earth rotates on an axis through its poles. The distance from the axis to a location on Earth at 40° north latitude is about 3033.5 miles. Therefore, a location on Earth at 40° north latitude is spinning on a circle of radius of 3033.5 miles. Compute the linear speed on the surface of Earth at 40° north latitude.

Short Answer

Expert verified

The linear speed on the surface of the earth at $40 °$ in the north latitude is 794 miles/hours.

Step by step solution

Step 1. Given information.

Consider the given information,

The distance from the axis to a location on Earth at 40° north latitude is about 3033.5 miles. Therefore, a location on Earth at 40° north latitude is spinning on a circle of radius of 3033.5 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 40 degrees.

$\begin{array}{rcl} t & = & \frac{24 hours}{360 °} \times 40 ° \\ = & \frac{24 hours}{9} \\ = & \frac{8}{3} hours \end{array}$

Convert the angle 40 degrees into radian.

$\begin{array}{rcl} θ & = & 40 ° \times \frac{π}{180 °} \\ = & \frac{2 π}{9} \end{array}$

Step 3. Find the linear speed.

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

$v = \frac{θ}{t} \cdot r$

Substitute the angle $\frac{2 π}{9}$ , time is $\frac{8}{3} hours$ and the radius is 3033.5 miles. Substitute the values in the formula,

$\begin{array}{rcl} v & = & 3033.5 \times \frac{\frac{2 π}{9}}{\frac{8}{3}} \\ = & 3033.5 \times \frac{6 π}{72} \\ \approx & 794 miles / hours \end{array}$

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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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