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Vector Basics - Example 3

In mathematics, a vector (from the Latin "mover") is a geometric object that has a magnitude (or length) and a direction. Vectors can be added to other vectors according to vector algebra, and can be multiplied by a scalar (real number). Vectors play an important role in physics, especially physics and astronomy, because the velocity and the momentum of an object are expressed by vectors.

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Okay, So planes flying 30 degrees north of beast at 500 MPH said this way. That's what the specter is representing and then encounters a jet stream that pushes it to south at 20 MPH. So that's this vector This way. So what is the new speed and direction of the plane? Okay, so if we recall, we can actually find the resulting vector from this picture so we can just copy factors that so our new vector will be somewhere out there. I mean, that may not be to scale, but that's kind of the idea. Have a vector going this way and vector going this way, and then the resulting vector is gonna be out there. So I just want to add these two vectors together, and I want to utilize for this underlining coordinate system. So if I just have my standard X y plane coordinates, then what I have is I'm adding the vector well. This 500 MPH has a component in the horizontal, which is 500 co sign of 30 and then a component in the vertical, which is 500 time sign of 30. It's the right triangle right here, and I'm adding this other velocity vector, which is Onley in the vertical zero in the horizontal. And it's actually negative 20 because it's pointing down. So my velocity vector is just gonna be the some of these two vectors, which is going to be 2, 50 times the square root of three. So I just I use my values for Coastline 30 and 7 30 and this is gonna be 2 50 minus 20 to 30. So there's my resulting vector and now the length of the specter. So my new speed, it's just gonna be the length of this vector tricking. Just throw in our calculator, which is 20 times the square root of 601 which, well, that's approximately 4 90 0.306 It's per hour and then our direction, so we can either just normalize this specter. But it might be a little bit better to sort of say, as an ankle, you know, north of east or south of east or whatever it is. And so the angle just a little bit trigonometry is gonna be the inverse tangent of 2 30 over 2 15. Group three tangent is opposite over Jason, and this gives us well, approximately 27 point 97 56 and this is degrees and they will still be in north of east.

Georgia Southern University
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Lily A.

Johns Hopkins University

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Baylor University

Kristen K.

University of Michigan - Ann Arbor

Samuel H.

University of Nottingham

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