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A woman walks due west on the deck of a ship at 3 mi/h. The ship is moving north at a speed of 22 mi/h. Find the speed and direction of the woman relative to the surface of the water.

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$$22.2 \mathrm{mi} / \mathrm{h}, \mathrm{N8}^{\circ} \mathrm{W}$$

01:55

Wen Zheng

02:08

Carson Merrill

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 2

Vectors

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Lectures

02:56

In mathematics, a vector (from the Latin word "vehere" meaning "to carry") is a geometric entity that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. Vectors play an important role in physics, engineering, and mathematics.

11:08

In mathematics, a vector (from the Latin word "vehere" which means "to carry") is a geometric object that has a magnitude (or length) and direction. A vector can be thought of as an arrow in Euclidean space, drawn from the origin of the space to a point, and denoted by a letter. The magnitude of the vector is the distance from the origin to the point, and the direction is the angle between the direction of the vector and the axis, measured counterclockwise.

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the problem states that a woman walks due west on the death of A ship at three mph. The ship is moving not at the speed of 22 miles further. Find the speed and direction of the women related related to the surface of the important. All right. So now we can right here that let the speed of the women do first on the deck of the ship is represented by O A. In the diagram, right form A. We can say speed of the ship to the due to north is represented by Obi. Right ship is moving in this way. Okay, So now or what we need to find is we need to find the Lawrence speed and direction of the women related to the services. Okay. Yeah. So now what we can do here, we will form a form a right Yeah, we will draw a C. Yeah, equal to or parallel to. You can say equal to a panel to rate This is Koby. Yes. So a C. Is equal to O. B. Is equal to 22 MPH. Can we say this? Yes. So now let C O A B. We have supposed to like, okay, so now the speed of this ship, we can say in right angle. We know that is part of this shit. You do not represented by Obi only right? This is the direction of ship. All right. We need to find hell Tito. Yeah. Great. You need to find your tree to Yes. So now in right angle triangle. Can we say that this is a right angled triangle and this is right angle all are we are taking right angled triangle. Right? So you're strangled or ceo We will use pattern for the students. So all C square. That is how important is the square is equal. Superabundance, cooler squared plus basis where that is always square first A C squared. So this will give us what? This is three miles. And this is 22 miles. So we will just square it and we will get Aussie Oh see right. So O. C. Will be one Or she will be for 96 or they will be wrote over for 93 3. So that will give us 22.2 mi for that. So this is the speed of the women jake. Mhm. This is the speed of development. We have found out this is the first answer and we will find no direction. So for direction, direction, we should also find out or the angle of a theta and alpha. Right? So basically we need to find the tita that is making with the surface of water. Right? Right. So the speed of women. The native to the surface of water is 22 .2 mi. But say So this is first part and 42nd birthday letters right here. This is for the first path. Right now, for the second part we will take again the triangle. See you. So, can we find your tanta. Tanta is nothing but a particular upon based So here's a particular is a C. And basis you so 22 by three. Right? That will give us 7.33. And the tree to will be 82.33 or approximately equals two 82 point. You can say 82 degrees. Now this is the idea to write this is to to we have got that is 82 degrees right? Can you see here in the diagram? Yes. So to find the Elva say to find the alfa, we will just subject deep uh angle tita vine and predicted it. So alfa can also be written as L. fucking also be witness 90 -2 years object. So here we will get 99 32. It was to a degree. So the women has a speed of 22.2 mph related to the surface of water. And its direction is no eight degrees. The best that means the you can say from the north it is to the best you can say it is north from the north to the best it will be a degree. Right? So this is it. Answer to this problem. I hope you understood it on concept. Thanks for watching

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