The earth rotates about its axis once every 23 h 56 min 4 s, and the radius of the earth is 3960 mi. Find the linear speed of a point on the equator in mi/h. (Round your answer to two decimal places.)

To find the linear speed of a point on the equator, we can use the formula for linear speed:

\[
v = \frac{d}{t}
\]

where:
- \( v \) is the linear speed,
- \( d \) is the distance traveled,
- \( t \) is the time taken.

### Step 1: Find the distance traveled (Circumference of Earth)
Since the Earth is approximately a sphere, the distance traveled by a point on the equator during one full rotation is the circumference of the Earth. The formula for the circumference \( C \) of a circle is:

\[
C = 2 \pi r
\]

Given:
- Radius \( r = 3960 \) miles,
\[
C = 2 \pi \times 3960
\]

### Step 2: Convert the time period to hours
The Earth completes one rotation in 23 hours, 56 minutes, and 4 seconds. We convert this time into hours:

\[
t = 23 + \frac{56}{60} + \frac{4}{3600}
\]

### Step 3: Calculate the linear speed
Using the formula \( v = \frac{C}{t} \), we will compute the linear speed in miles per hour.

Let me calculate this now.The linear speed of a point on the equator is approximately **1039.57 miles per hour**.

Do you need more details or have any questions about this calculation?

Here are 5 related questions to explore:

1. What is the angular speed of the Earth in radians per second?
2. How would the linear speed change if the radius of the Earth increased by 10%?
3. How does the linear speed at the equator compare to that at a latitude of 45 degrees?
4. If the Earth's rotation period slowed down by 1 hour, what would be the new linear speed at the equator?
5. How would the linear speed differ if calculated in kilometers per hour instead of miles per hour?

**Tip:** To convert between linear and angular speed, remember that linear speed \(v = r \times \omega\), where \(r\) is the radius and \(\omega\) is the angular speed.

Discover how to calculate the linear speed of a point on the equator using geometry and trigonometry. This problem involves finding the circumference of the Earth and converting time units. Suitable for advanced high school students.

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