Imagine a 3-dimensional world with coordinates that are labeled with x, y, and z, as if you are in a large room with walls, a high ceiling and a floor. The edges are x, y and z with z up toward the ceiling, the flat plane floor is x-y.Starting at the origin, go along "x" 2 meters. Then go parallel to "y" 4 meters. Then go up parallel to "z" 3 meters. This point is somewhere in the room above the floor.What is the vector from the origin to the point?What is the magnitude of that vector? That is, what is its length?What angle does it make to the floor? This would be 90°-θ where θ is the angle down from the z azis. (Hint: Use the arctangent knowing z and the length of the vector.)If you dropped from that point directly down to the floor, how far would you fall?How long would it take, given that falling objects accelerate at 10 m/s every second (10 m/s2)?

If we start at the origin and then move along "x" 2 meters, Then parallel to "y" 4 meters, and…

Answered: Imagine a 3-dimensional world with…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Imagine a 3-dimensional world with coordinates that are labeled with x, y, and z, as if you are in a large room with walls, a high ceiling and a floor. The edges are x, y and z with z up toward the ceiling, the flat plane floor is x-y.

Starting at the origin, go along "x" 2 meters. Then go parallel to "y" 4 meters. Then go up parallel to "z" 3 meters. This point is somewhere in the room above the floor.

What is the vector from the origin to the point?
What is the magnitude of that vector? That is, what is its length?
What angle does it make to the floor? This would be 90°-θ where θ is the angle down from the z azis. (Hint: Use the arctangent knowing z and the length of the vector.)
If you dropped from that point directly down to the floor, how far would you fall?
How long would it take, given that falling objects accelerate at 10 m/s every second (10 m/s²)?

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