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.