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The captain of a plane wishes to proceed due west. The cruising speed of the plane is 245 m/s relative to the air. A weather report indicates that a 38.0-m/s wind is blowing from the south to the north. In what direction, measured with respect to due west, should the pilot head the plane?

$\theta=8.82^{\circ},$ south of west.

Physics 101 Mechanics

Chapter 3

Kinematics in Two Dimensions

Motion in 2d or 3d

Cornell University

University of Michigan - Ann Arbor

University of Washington

Hope College

Lectures

04:01

2D kinematics is the study of the movement of an object in two dimensions, usually in a Cartesian coordinate system. The study of the movement of an object in only one dimension is called 1D kinematics. The study of the movement of an object in three dimensions is called 3D kinematics.

10:12

A vector is a mathematical entity that has a magnitude (or length) and direction. The vector is represented by a line segment with a definite beginning, direction, and magnitude. Vectors are added by adding their respective components, and multiplied by a scalar (or a number) to scale the vector.

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The captain of a plane wis…

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02:32

Go The captain of a plane …

01:22

The pilot of an aircraft w…

01:40

Velocity The speed of an a…

04:28

03:38

An airplane pilot wishes t…

04:06

(III) An airplane whose ai…

03:28

An airplane has a speed of…

05:00

All right, Uh, this video, we're gonna do problem number 60 on dhe. So we're trying to find what direction of plane would have to go if it wants to go straight west. And there's wind blowing from south to north. So the best way to do this is to literally draw a picture. So first, we're gonna have, like, a little compass, Almost. Okay, so we know that there's wind, so we're gonna represent windows. Blew when'd is going from. It's a simple himself to north. So this way we should write a bunch of little errors here, 38.0 meters per second, and then our plane is going to be green. Is going this way is going this way that 145 meters per second, right? So obviously, if you add these to the plane's going to be going north of west, not directly. This plane wants to travel directly west. So right now, if we're traveling straight west and then we get a gust of wind that's going south to north, we're gonna end up going northwest. But we only want to be going west. So what can we do? I'm gonna start a new page. So pretty much weaken draw vectors of what we have. So we're gonna draw our planes vector. We're traveling this way like this, and then we're gonna draw a wins vector going like this. So we know these. This is 38 meters per second for the wind. This is 245 meters per second for the plane. And in order to go directly west, we have to go slightly self because the wind is pointing us. They're gonna push us partially not So this actor here, this red vector that I'm about to draw is going to give us this angle was how far down relative to the west direction we're gonna have to go to travel directly west. So in other words, it's gonna have to be south of West. We're gonna have to travel a little bit. So for the West, um, direction. How are we gonna get that? So we're not looking. We're not gonna use price theory. In theory, I'm here because that tells us the length of this side and that'll tell us a relative speed. But we're not looking for that. We're looking for data so you erase that? We're looking for theater, so we're just gonna use simple Trig. Help us find them. So we have 38 meters per second. So from theatre, we have are opposite and we have irrigation set. So from so can tell. Well, we can use tangent and we know if we want to find an angle. If he's inverse tangent So 10 inverse of opposite over. Jason. Bert, we have our office inside. We have energies inside, so let's just put him into 10. 10 inverse of 38.0 meters per second, divided by 245 meters per second. Gives us our angle of So this is data equals, uh, 8.82 degrees. Okay, cool. So now we know from our little grid that we drew our little compass that we drew and the first lied this big thing. If word try with the plains traveling here at an angle, hear Sita or saint as 8.82 degrees, then the direction the wind is gonna push us is here, and we're gonna be traveling right where we want. We're gonna be traveling right along this line, right straight West so directly west. If we travel 8.82 degrees south of west Thanks for watching. I hope this video is helpful. Onda. Best of luck on any other problems you have.

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