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A jetliner can fly 6.00 hours on a full load of fuel. Without any wind it flies at a speed of $2.40 \times 10^{2} {m} / {s}$ . The plane is to make a roundtrip by heading due west for a certain distance, turning around, and then heading due east for the return trip. During the entire flight, however, the plane encounters a 57.8 -m/s wind from the jet stream, which blows from west to east. What is the maximum distance that the plane can travel due west and just be able to return home?

$x=2441.7 \mathrm{km}$

Physics 101 Mechanics

Chapter 3

Kinematics in Two Dimensions

Motion in 2d or 3d

Cornell University

Rutgers, The State University of New Jersey

Simon Fraser University

University of Sheffield

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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so the question states that a plane can travel at 240 meters per second when there's no wind, and in this case there is a jet stream blowing from west to east at 57.8 meters per second. We're also told that the plane can fly for six hours on a full, uh, fuel tank. Six hours is the same thing as to 21,600 seconds, and this will just be useful later. And so we're trying to find how far, uh, the plane can travel without running out of fuel. So this is pretty simple, actually. So when the when the plane is flying west, the speed it can travel at is 240 meters per second, minus the wind that's blowing on it, which is 57.8 meters per second. That's because the wind is going against its motion of travel, which is in this direction. So 240 minus 57.8 is equal to 182 0.2 meters per second in the east west direction. Now, when the plane is traveling in the west to east direction, it's moving with the wind, so it's 240 plus 57.8 meters per second. So the speed is 297.8 meters per second in the west east direction. So now that we know this, um we can figure out the, uh, time are the distance that the plane can travel. So we know from our Kitimat equations that the velocity times time is equal to the distance where the time is also equal to the distance divided by the Basti. And we know that the total time that the plane can travel let's just call it T for now is equal a T. So the total time the plane can travel should be equal to the distance that the plain travels in the West direction divided by its speed plus the distance. He travels in the east direction divided by its speed, and this will give us the total time. So we know the total time is 21 21,600 seconds. And we also know the, um speed and moves in the West direction and the east direction So 182.2 meters per second as well as 297.8 meters per second. So now all we have to do is so for what X is equal to, um And to do this, we can just, uh, take 21,600 and divide by one over on the 182.2 course one over 297.8. And one other thing. These exes are the same because it has to travel the same distance this way and on the way back, because it's a a round trip. So when we do this, we find that X is equal to around, um 200. Sorry, not to 1 202,400 41 0.6 62 kilometers, and this is the final answer.

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