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What are the direction and magnitude of your total displacement if you have traveled due west with a speed of 23 $\mathrm{m} / \mathrm{s}$ for 175 $\mathrm{s}$ ,then due south at 12 $\mathrm{m} / \mathrm{s}$ for 285 $\mathrm{s}$ ?

$\vec{s}$ has a magnitude of $[5281.7 \mathrm{m}]$ and makes an angle of $\left[220.35^{\circ}\right]$ with positive $x$ -axis.

Physics 101 Mechanics

Chapter 3

Vectors in Physics

Physics Basics

Cornell University

University of Michigan - Ann Arbor

University of Winnipeg

Lectures

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We're traveling to west at a speed of 23 meters per second for 125 175 seconds and then due south at 12 meters per second for 285 seconds. Here I've notated the two directions that were movie with red and green respectively. And first let's go ahead and try and find how far removed in the ex direction. And then how far removed in the wind direction for the X direction, removing at a speed of 23 meters per second for 175 seconds. This gives us a displacement of 4025 meters. Notice this is in the negative X direction because the speed here should be negative. So we have negative 40,000 and 25 meters now for the widest placement. We have a movement with a speed of negative 12 meters per second because we're moving in the negative direction for 285 seconds. This gives us a why displacement of negative 3420 meters and now we can use these two accent. Why components to find the displacement vector, its magnitude and its direction here. We already have a right triangle. So all we need to do is find the punters here. The hype oddness is equal to the square root of X squared plus y square. Where have you playing in the numbers? You're just d'oh negative 4025 meters squared, plus negative 3420 meters square. That gives us about 5282 meters, which would be the magnitude of the displacement vector to find the angle angle we're after is this angle which will notice data they were called Data can be solved by using the interest engine function of why over hacks. Here we have tangent of negative 34 to 0 meters over negative for 0 to 5 meters and that will give us an angle of 40 degrees. But notice 40 degrees is pointing in this direction. So we need to go ahead and add 180 degrees to Orion. Uh, 220 degrees

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