A nautical mile equals the length of arc subtended by a central angle of 1 minute on a great circle on the surface of Earth. If the radius of Earth is taken as 3960 miles, express 1 nautical mile in terms of ordinary, or statute, miles.
Around the earth is 360*60 = 21600 minutes of arc or nautical miles.
2 pi (3960) = 24881 landlubber miles around the earth
24881/(360*60) = 1.152 landlubber miles/ nautical mile
Why did the sailor go to the comedy club? Because he wanted to hear some nautical laughs! Now, let's set sail to solve this problem.
Given that 1 nautical mile is the length of arc subtended by a central angle of 1 minute on a great circle on Earth's surface, we need to find out how many ordinary, or statute, miles are equivalent to 1 nautical mile.
To do that, we first need to determine the circumference of Earth in nautical miles. The formula for calculating the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.
So, the circumference of Earth in nautical miles is C = 2π(3960) = 7920π nautical miles.
Now, we can set up a proportion to find the equivalent value in statute miles:
1 nautical mile is to 7920π nautical miles as x statute miles is to 7920π nautical miles.
Simplifying the proportion, we get:
1/7920π = x/7920π.
Cross-multiplying, we find:
x = 1.
Therefore, 1 nautical mile is equivalent to 1 statute mile.
So, if you were expecting a funnier punchline, I'm sorry to disappoint. But now you know that 1 nautical mile is equal to 1 statute mile!
To express 1 nautical mile in terms of ordinary, or statute, miles, we need to determine the length of one minute of arc on a great circle on the surface of Earth in miles.
The circumference of a circle is given by the formula C = 2πr, where r is the radius. In this case, the radius of Earth is 3960 miles.
To find the length of one minute of arc on the surface of Earth, we divide the circumference of Earth by 360 (since there are 360 degrees in a circle) and then further divide by 60 (since there are 60 minutes in a degree):
Length of one minute of arc = (2π * 3960 miles) / (360 * 60)
Now we can calculate the value:
Length of one minute of arc = (2 * 3.14159 * 3960 miles) / (360 * 60)
Length of one minute of arc ≈ 1.1515 miles
Therefore, 1 nautical mile is approximately equal to 1.1515 ordinary, or statute, miles.
To express 1 nautical mile in terms of statute miles, we need to first understand the relationship between nautical miles and the circumference of the Earth.
The circumference of a circle can be found using the formula C = 2πr, where C represents the circumference and r represents the radius. In this case, the radius of the Earth is given as 3960 miles.
However, since we are dealing with the length of arc subtended by a central angle of 1 minute on a great circle, we need to convert this angle to radians. There are 60 minutes in a degree and 2π radians in a full circle, so there are (60/360) * 2π radians in a 1-minute angle.
Using the formula for arc length, s = rθ, where s represents the arc length, r represents the radius, and θ represents the angle in radians, we can substitute the values to find the length of the arc for a 1-minute angle:
s = (3960 miles) * [(60/360) * 2π radians]
= (3960 miles) * (1/6) * (2π radians)
Simplifying this expression gives us:
s = 2π * (3960/6) miles
= 2 * 22/7 * 660 miles [Using an approximation of π as 22/7]
≈ 2088.5714 miles
Therefore, 1 nautical mile is approximately equal to 2088.57 statute miles.