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 for the circumference of a circle.
a. The formula to calculate the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. In this case, the radius of the Earth at the equator is given as 6380 km.
So, the circumference of the Earth at the equator is C = 2π(6380 km).
To find the speed, we need to divide the circumference by the time it takes for one complete rotation. The time for one complete rotation is about 24 hours, or 24 x 60 x 60 seconds.
Speed = Circumference / Time
Substituting the values, we get:
Speed = 2π(6380 km) / (24 hours x 60 minutes x 60 seconds)
To convert km/hour to m/second, we need to multiply the speed by 1000/3600. This is because there are 1000 meters in a kilometer, and 3600 seconds in an hour.
So, the final formula for speed at the equator is:
Speed = 2π(6380 km) / (24 hours x 60 minutes x 60 seconds) x 1000/3600
Now let's calculate it.
Speed = 2π(6380 km) / (24 hours x 60 minutes x 60 seconds) x 1000/3600
≈ (2 x 3.14 x 6380 km) / (24 x 60 x 60 seconds) x 1000/3600
≈ (12760π km) / (86400 seconds) x 1000/3600
≈ 7.9 km/s (approximately)
So, the speed of an object at the equator due to the Earth's rotation is approximately 7.9 km/s.
b. To convert this speed to miles/hour, we need to multiply the speed by a conversion factor.
1 kilometer = 0.621371 miles
1 hour = 3600 seconds
So, the conversion factor is (0.621371 miles / 1 kilometer) x (3600 seconds / 1 hour) = 2236.936292 miles/hour.
Now, let's calculate it.
Speed (in miles/hour) = Speed (in km/s) x Conversion Factor
Speed (in miles/hour) = 7.9 km/s x 2236.936292 miles/hour
≈ 17636.5823 miles/hour (approximately)
So, the speed of an object at the equator due to the Earth's rotation is approximately 17636.5823 miles/hour.