Question

New York is roughly 3000 miles from Seattle. When it is 10:00 A.M. in Seattle, it is 1:00 P.M. in New York. Using this information, estimate (a) the rotational speed of the surface of Earth, (b) the circumference of Earth, and (c) the radius of Earth.

Answer 1

I understand that the time difference around the globe is about 24 hours, and there is a 3 hour time difference between NY and Seattle.

(NY-Seattle)/(total) = 3/24 = 1/8th the circumference of the earth.

And somehow i could use arc length to find the circumference of the earth... but how?

Answer 2

Okay so you got the first step! Good job :)

To find the circumference all you have to do is multiply 8 * 3000! What does that equal? Do you know the next step?

Answer 3

Okay now I got it! :D

Answer 4

Why would you multiply by 8 though? Where did it come from? :o

Answer 5

ITs the the 1/8th you found earlier

Answer 6

Let us say that the first sun's rays hit Seattle and then takes 3 hours to travel down to NY which is a distance of 3000 miles along the circumference of the earth!
Okay?
So If distance = 3000 miles
Time = 3 hours!
And the sun stays still!
then speed of earth's rotation = 3000/3 = 1000miles/hour

Answer 7

Is there a formula? x_x

Answer 8

Another way to find it is the Earth travels 24 at 1,000 miles per hour it would be 24000, which is also the same thing i found earlier.

with this you do c=pi*24

Answer 9

OH. D=rt.

Answer 10

Good job on finding out the 1/8 part!
So we know that 3000 miles is 1/8 of the circumference of the earth!
So
The cicumference = 3000 * 8 = 24000 miles!
And thus the radius would be = 2*pi*r = 24000
Find r! :D
Did you get this? :D

Answer 11

Ash, how did YOU get the 1000 mph?

Answer 12

ITs the the 1/8th you found earlier

Answer 13

Noooo... im trying to put it into an equation format x_x its not...connecting.

Answer 14

Which PART did you not get?
Specifically?

Answer 15

Just or Info. the circumference is actually the Equator.

Answer 16

Why am i not multiplying 1/8 (3000)? why is it 8 * 3000..

Answer 17

Because 3000 is a part of the EQUATOR[Circumference]

Answer 18

Let the total equator = x
Thus
Seattle to NY = 3000 miles which is 1/8 of x
So
x = 8*3000 = 24000 miles is the equator or the circumference! :D

Answer 19

Oh my goodness... -_- lol i get it now :D

Answer 20

And also Seattle and New York are kinda on the same lattitude so...!

Answer 21

Okay.
3000mi/3hours=1000 mi/hr

then, 24hrs*1000mi/hr=24000mi

with the equation i gave earlier it comes around to be 24000 mi/6.28 which would eqaul out to 3822.

Answer 22

Great! :)

Answer 23

I was just kinda babbling on like a crazy person through out this thing, sowwy

Answer 24

Okay.
3000mi/3hours=1000 mi/hr

then, 24hrs*1000mi/hr=24000mi

with the equation i gave earlier it comes around to be 24000 mi/6.28 which would eqaul out to 3822.

Answer 25

I wasnt understanding what it meant when it said the distance = 1/8 of the circumference. Haha.

Answer 26

:D

Answer 27

Yes! Thank you @Ashleyisakitty and @AkashdeepDeb :)

Answer 28

:)

Answer 29

^_^