Math Help - Latitude and Radius of the Earth

1. Latitude and Radius of the Earth

If the radius of the earth is 4000 mi,

(a) How far is Fort Worth, Texas (latitude 33 N), from the equator?

(b) How far is Fort Worth from the North Pole?

(c) Fort Worth is due south of Winnipeg, Manitoba (latitude 50 N). What is the distance between them?

(d) Find the linear speed, due to the rotation of the earth, of Winnipeg.

2. Re: Latitude and Radius of the Earth

Originally Posted by joshuaa
If the radius of the earth is 4000 mi,

(a) How far is Fort Worth, Texas (latitude 33 N), from the equator?

(b) How far is Fort Worth from the North Pole?

(c) Fort Worth is due south of Winnipeg, Manitoba (latitude 50 N). What is the distance between them?

(d) Find the linear speed, due to the rotation of the earth, of Winnipeg.
1deg along a great circle = 2pi4000/360 miles
A point on earth latitude L moves in a circle radius =cos L*4000

3. Re: Latitude and Radius of the Earth

Why does a point on earth Latitude L moves in a circle, radius= cos L*4000?

Why not sin L*4000, or tan L*4000? Also, does this latitude mean it is above the earth surface?

4. Re: Latitude and Radius of the Earth

Originally Posted by joshuaa
Why does a point on earth Latitude L moves in a circle, radius= cos L*4000?

Why not sin L*4000, or tan L*4000? Also, does this latitude mean it is above the earth surface?
a point of latitude is on the surface of the earth.
Radius of latitude circle at 50 deg N equals cos50* 4000 miles or sin 40*4000 miles

5. Re: Latitude and Radius of the Earth

Since we are talking about a moving point on the Circle, this is going to solve question (d).

v = rw = 4000 cos 50 (rev / 24 hours)

Am I doing ok?

6. Re: Latitude and Radius of the Earth

Originally Posted by joshuaa
Since we are talking about a moving point on the Circle, this is going to solve question (d).

v = rw = 4000 cos 50 (rev / 24 hours)

Am I doing ok?
You have to calculate the radius to circumference and then divide by 24 to get velocity in miles per hr

7. Re: Latitude and Radius of the Earth

This means

v = 4000 cos 50 (rev / 24 hours) (2Pi / rev) = 673 mi/h (rounded to 3 figures)

8. Re: Latitude and Radius of the Earth

Can anyone help me to solve the Problems from (a) to (c)?

9. Re: Latitude and Radius of the Earth

Hey Teachers and Professors! Anyone there?

10. Re: Latitude and Radius of the Earth

radius of earth = 4000 miles
circum/4 = 90 degrees
solve for a,b,c

11. Re: Latitude and Radius of the Earth

You've already been given plenty of help. In the very first response, BJHopper said "1deg along a great circle = 2pi4000/360 miles"
so 35 degrees latitude is what distance above the equator? Once you have answered (a), (b) is easy- The distance from the equator to the north pole is, of course, 1/4 the circumference of the earth so to find the distance from Fort Worth to the north pole, subtract its distance from the equator from that. (c) is equally easy. Use the same ideas to find the distance from the equator to Manitoba and subtract the distance from the equator to Fort Worth.

He also said "A point on earth latitude L moves in a circle radius =cos L*4000". You can use that to answer (d).

12. Re: Latitude and Radius of the Earth

(35*2*4000*Pi) / 360 = 2443 miles

I don't Understand why does the book say the answer is 2300 miles.

[ (90*2*4000*Pi) / 360 ] - 2443 miles = 3840 miles

The book says 4000 miles. This result makes sense if rounded to 1 figure. Unlike the mysterious answer of (a)

[ (50*2*4000*Pi) / 360 ] - 2443 miles = 1047 miles

Again, I have no idea why the book says 1200 miles.

13. Re: Latitude and Radius of the Earth

Originally Posted by joshuaa

(35*2*4000*Pi) / 360 = 2443 miles

I don't Understand why does the book say the answer is 2300 miles.

[ (90*2*4000*Pi) / 360 ] - 2443 miles = 3840 miles

The book says 4000 miles. This result makes sense if rounded to 1 figure. Unlike the mysterious answer of (a)