# Math Help - could you explain it in drawing please

1. ## could you explain it in drawing please

1. Because of the rotation of the earth, the surface at the equator
moves 463 meters per second. The speed of the earth’s surface
rotation is less at higher latitudes and is zero at the poles. The
radius of the earth is 6373 km. Determine the speed of the
earth’s rotation at latitudes 20 degree celcius and 70 degree celcius.
Hint: Consider how the circumference of the earth, and hence
the distance travelled, will change with latitude.

I've laughed pretty hard, but not usually quite as hard as that. Are you SURE you mean "degree celcius"?! Careful what you type.

Okay, now without the "celcius", one needs to determine the radius at the given latitude. This is no problem with just a little trigonometry.

Draw a circle.
Put in a horizontal diameter representing the side view of the Equator.
Point out the Center. Call it point "O".
Label half this diameter 6373 km.
Put in another Radius somewhere between the equator and a Pole.
Label this new radius 6373 km (We just assumed the earth is a perfect sphere. Oh, well.)
Lable the point of intersection of the new radius and the circle "A".
Construct a line segment perpendicular to the Equator and to point "A".
Label the point where the new line segment intersects the Equator "B".

Notice a couple of things.

Triangle ABO is a Right Triangle.
Angle BOA is your lattitude measurement.
You need only a cosine to calculate the length of OB.

orsonik: I do not quite get this. can anybody draw it so I can see and explain a bit detailed???

2. Originally Posted by orsonik
1. Because of the rotation of the earth, the surface at the equator
moves 463 meters per second. The speed of the earth’s surface
rotation is less at higher latitudes and is zero at the poles. The
radius of the earth is 6373 km. Determine the speed of the
earth’s rotation at latitudes 20 degree celcius and 70 degree celcius.
Hint: Consider how the circumference of the earth, and hence
the distance travelled, will change with latitude.

I've laughed pretty hard, but not usually quite as hard as that. Are you SURE you mean "degree celcius"?! Careful what you type.

Okay, now without the "celcius", one needs to determine the radius at the given latitude. This is no problem with just a little trigonometry.

Draw a circle.
Put in a horizontal diameter representing the side view of the Equator.
Point out the Center. Call it point "O".
Label half this diameter 6373 km.
Put in another Radius somewhere between the equator and a Pole.
Label this new radius 6373 km (We just assumed the earth is a perfect sphere. Oh, well.)
Lable the point of intersection of the new radius and the circle "A".
Construct a line segment perpendicular to the Equator and to point "A".
Label the point where the new line segment intersects the Equator "B".

Notice a couple of things.

Triangle ABO is a Right Triangle.
Angle BOA is your lattitude measurement.
You need only a cosine to calculate the length of OB.