00:01
So we can draw what's going on here.
00:03
First, we can draw a circle modeling earth.
00:09
And let's take a quarter.
00:12
So we know that this distance here is r.
00:15
We're going to draw a piece going out.
00:20
We're going to say that this angle here is theta.
00:24
And then we're going to draw another line going this line.
00:28
We're going to say that due to the vertical angle theorem, this is going to be also theta.
00:35
And we know that this right here, this piece right here tangentially to the rather adjacent to this angle is going to be radius r.
00:47
And we can say that r is going to be equal to the radius of the earth times cosine of theta, where theta would be the latitude at which you are evaluating.
00:59
We know that the earth rotates at one revolution for every one day, and we can say that omega equals 2 pi over t.
01:11
We know that the radius of the earth is also equaling to 6 .38 times 10 to the 6th meters.
01:20
So if we wanted to find the tangential, the linear velocity at the equator for part a, we can say that v equals r rather omega r sub e and this is going to be two time two pi r sub e divided by t and this is equaling two pi for every one day we know that there is one day in every 86 ,400 seconds and then times the radius of the earth i'll try to fit it here my apologies 6 .38 times 10 to the 6 meters.
02:08
And so this v is going to be equal to approximately 464 meters per second...