X Consider a vector E pointed into the second quadrant' of the Cartesian x-y coordinate plane, as pictured above. Consider the vector E pictured above and assume it is meant to represent some physical vector quantity we're studying. Since I've not specified what sort of physical quantity this vector is supposed to represent (perhaps it might be a force vector, a velocity vector, etc.), we'll leave it vague (but also recognize that the numerical values we record for physical quantities typically have units of measurment) and we'll just say that its units are simply called units. Suppose the magnitude, E, of E is given by E = 30.00 units, and suppose the angles drawn in the above figure are given by 0 = 60.00° and ø = 30.00°. (a.) What are the x- and y-components of vector E, pictured above, in terms of the angle 0 and the magnitude E? (b.) For the same vector, what are the x- and y-components in terms of the angle ø and the magnitude E? (c.) What would these vector components be if the magnitude of E was doubled?

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Chapter1: Units, Trigonometry. And Vectors
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Problem 2.
Vectors
y
0,
X
Consider a vector E pointed into the second quadrant' of the Cartesian x-y coordinate plane, as pictured above.
Consider the vector E pictured above and assume it is meant to represent some physical vector quantity we're studying.
Since I've not specified what sort of physical quantity this vector is supposed to represent (perhaps it might be a force
vector, a velocity vector, etc.), we'll leave it vague (but also recognize that the numerical values we record for physical
quantities typically have units of measurment) and we'll just say that its units are simply called units.
Suppose the magnitude, E, of E is given by E = 30.00 units, and suppose the angles drawn in the above figure are given
by 0 = 60.00° and ø = 30.00°.
(a.) What are the x- and y-components of vector E, pictured above, in terms of the angle 0 and the magnitude E?
(b.) For the same vector, what are the x- and y-components in terms of the angle o and the magnitude E?
(c.) What would these vector components be if the magnitude of E was doubled?
Note: You can check your answers to these kinds of problems by simply using the x- and y-components you found and
plugging them into the appropriate formulae for vector magnitude (which comes from the Pythagorean Theorem) and
direction angle (which comes from the trigonometric TOA rule).
'Note: The Cartesian x-y coordinate plane is split into 4 regions which we call quadrants, and we frequently label these quadrants
with roman numerals in a counter-clockwise order from the +x-axis:
• Quadrant I is the region where the x and y coordinates are both positive: x > 0 and y > 0,
• Quadrant II is the region where the x coordinates are positive and the y coordinates are negative: x > 0 and y < 0,
• Quadrant III is the region where the x and y coordinates are both negative: x < 0 and y < 0,
• Quadrant IV is the region where the x coordinates are negative and the y coordinates are positive: x < 0 and y > 0.
Transcribed Image Text:Problem 2. Vectors y 0, X Consider a vector E pointed into the second quadrant' of the Cartesian x-y coordinate plane, as pictured above. Consider the vector E pictured above and assume it is meant to represent some physical vector quantity we're studying. Since I've not specified what sort of physical quantity this vector is supposed to represent (perhaps it might be a force vector, a velocity vector, etc.), we'll leave it vague (but also recognize that the numerical values we record for physical quantities typically have units of measurment) and we'll just say that its units are simply called units. Suppose the magnitude, E, of E is given by E = 30.00 units, and suppose the angles drawn in the above figure are given by 0 = 60.00° and ø = 30.00°. (a.) What are the x- and y-components of vector E, pictured above, in terms of the angle 0 and the magnitude E? (b.) For the same vector, what are the x- and y-components in terms of the angle o and the magnitude E? (c.) What would these vector components be if the magnitude of E was doubled? Note: You can check your answers to these kinds of problems by simply using the x- and y-components you found and plugging them into the appropriate formulae for vector magnitude (which comes from the Pythagorean Theorem) and direction angle (which comes from the trigonometric TOA rule). 'Note: The Cartesian x-y coordinate plane is split into 4 regions which we call quadrants, and we frequently label these quadrants with roman numerals in a counter-clockwise order from the +x-axis: • Quadrant I is the region where the x and y coordinates are both positive: x > 0 and y > 0, • Quadrant II is the region where the x coordinates are positive and the y coordinates are negative: x > 0 and y < 0, • Quadrant III is the region where the x and y coordinates are both negative: x < 0 and y < 0, • Quadrant IV is the region where the x coordinates are negative and the y coordinates are positive: x < 0 and y > 0.
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