In this problem, we're going to find how far hurricane is from where it started after a certain amount of time. During this time, the hurricane will have two distinct motions. Let's look at those two motions here. First part of the motion, it'll be traveling 41 clamors per hour For three hours and at an angle of 60° north of West. Then It travels 25 commerce Prowar 1.5 hours due north. So we want to find out how far at the end of this is the hurricane relative to where it began. Just a note. This is not the distance it travels, as I mentioned that more about that later. So let's draw out the actual displacements. So we started the origin, going to be moving Along the line 60° to a point here. Now, displacement factors by definition are drawn from the starting point To the ending point of that particular motion. So this is T. one dissuasion factor. Now We were always v. one vector always, we're always moving 6° North or West. So that means this displacement factor also Is 60° northwest. Now we travel to north For 1.5 hours we get to this point. So my dissuasion vector here is that vector completely vertical. And again back to the concept are the sweating factor. It's drawn from where you began to where you ended up. So this is the total. Does not care how you got to. End point displacement is drawn directly from starting the final point. Now, if we look at this diagram looks to me, doesn't matter if you use triangle rule this add vectors, parallelogram rule. It looks to me the D. Toto factor is the one factor Plus T. two factors. So what this problem is gonna come down to is being able to elaborate on the components of D one, D. Two and get the components of the total. And then we can find the length of the total. Now, before I go back and find the components, let's just understand we no, from a standpoint of distance, How long the one vector is just from a physics standpoint. T one is going to be for t v one time delta T one. That's going to be links Of the one doctor. And because we always are moving during that interval At an angle 60° that The one and V one are in the same direction and the way we write that maybe right, that is the one factor the one vector delta T. What in this one simple statement, it has The relationship between the magnitudes just wrote T one, B 1, Delta T one. And it also says they are in the same direction. Likewise, D two Would be V2.52 in terms of it For the length of D two vector. And that means D. To vector Would be the two factor Got to T. two. So before we can actually now work on di tutto we need to go back and get our components. So let me go back to the triangle for view one. It's going to be the one why? It's gonna be v. one x. The second quadrant vector, meaning that you must move in negative X. First and then positive. Wide. To construct the vector. So V one X. is going to be negative. The one act is the adjacent to the 60° angle. So it's going to be minus the one co sign 60 And be one. Why? Why is the opposite side to the angle? It's going to be V one sign 60 degrees. The two is easier. I don't want to do anything in extra constructed So V two X 0. The two. Why? To construct the vector? I gotta moving positive. Why? The full length of the vector? So that means V. Two, Y. Is V. Two. So we have our components now. So now we can look at the total the total X. Is going to be D one, X plus T. To uh to Do you want X was 22 x. Which is equal to the one, X. To T. One Plus v. two. X doubt the T. Too. But I told you V two X zero. So this term does not contribute. So this would become -31 Co sign 60° delta T one. And putting in our numbers 41 -41 km Krauer Coast side of 60° three hours. This works out to be -61.5 km Now. Likewise for D. two. He toto. Why? This is gonna be V. One, Y delta T. One Plus v. two. Why Got to T. 2? So this is the one sign 60 degrees, There are 31 plus the two Times Delta T. two. And then we give myself some room here And putting in our numbers 41 kilometers per hour, sign 60 degrees three hours plus 25 km/h, hours. This works out to be 140 for kilometers, that's the Y. Component. So we now have the components, so we really have all the sides of the right triangle to use segments here. Um You know, here is here is D. Toto, you told her why the total X. So just forget about the arrows and anything like that. All we care about our decides now so we can use the Pythagorean theorem to get the total, so t total the man to the vector, the length of the hypothesis is going to be -61.5 km squared plus 1 44 kilometer square, And this works out to be 157 kilometers. That is how far you are relative to where you began again. As I mentioned, it is not the distance you travel, it's not odometer reading, and that's the whole problem.