Take the radius of the earth at the equator to be 6380 km

a. Find the speed the speed of an object at the equator due to the earth's rotation. ___m/s
b. Convert this speed to miles/hour (show your conversion factor in your written backup). __miles/hour

To find the speed of an object at the equator due to the Earth's rotation, we can use the formula:

Speed = 2πr / T

Where r is the radius of the Earth and T is the period of rotation.

a. Speed at the Equator (in meters/second):
Radius of the Earth (r) = 6380 km = 6380000 meters (since 1 km = 1000 m)
Period of Earth's rotation (T) = 24 hours = 24 * 60 * 60 seconds (since 1 hour = 60 minutes, and 1 minute = 60 seconds)

Speed = 2π * 6380000 / (24 * 60 * 60)
Speed ≈ 1674.4 meters/second

b. Converting speed to miles/hour:
To convert from meters/second to miles/hour, we use the conversion factor:

1 mile = 1609.34 meters
1 hour = 3600 seconds

Conversion factor: (1609.34 meters / 1 mile) * (1 hour / 3600 seconds)

Speed (in miles/hour) = 1674.4 * (1 mile / 1609.34 meters) * (1 hour / 3600 seconds)
Speed ≈ 3726 miles/hour

To find the speed of an object at the equator due to the Earth's rotation, we can use the formula v = ω * r, where v is the speed, ω is the angular velocity, and r is the radius.

a. First, we need to find the angular velocity. We know that the Earth completes one full rotation in approximately 24 hours. To convert this to seconds, we multiply by 60 (minutes in an hour), then by 60 (seconds in a minute):

Angular velocity (ω) = 2π radians / (24 hours * 60 minutes * 60 seconds)
= 2π radians / (86,400 seconds)
≈ 0.0000727 radians/second

Next, we substitute the given radius of the Earth at the equator, which is 6380 km (or 6,380,000 meters), into the formula:

v = ω * r
≈ 0.0000727 radians/second * 6,380,000 meters
≈ 463 meters/second

Therefore, the speed of an object at the equator due to the Earth's rotation is approximately 463 meters per second.

b. To convert this speed to miles per hour, we can use the conversion factor: 1 mile = 1609.34 meters and 1 hour = 3600 seconds.

First, we convert the speed from meters/second to kilometers/hour:
463 meters/second * 3600 seconds = 1,666,800 meters/hour
1,666,800 meters/hour ÷ 1000 = 1666.8 kilometers/hour

Then, we convert the speed from kilometers/hour to miles/hour by using the conversion factor:
1666.8 kilometers/hour ÷ 1.60934 = 1036.82 miles/hour (rounded to two decimal places)

Therefore, the speed of an object at the equator, due to the Earth's rotation, is approximately 1036.82 miles per hour.

a) 2*pi*R(km)*(1000 m/km)

-------------------------
(24 h)*(3600 s/hr)

= ___ m/s

b) Multiply the m/s speed from (a) by
(3600 s/hr * 1 mile/1609 m)

It is important that you learn to do these conversions yourself.