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Vectors

# Vectors - adamkiewicz(ja28724 – Vectors – Morozova...

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Unformatted text preview: adamkiewicz (ja28724) – Vectors – Morozova – (11102) 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A certain corner of a room is selected as the origin of a rectangular coordinate system. If a fly is crawling on an adjacent wall at a point having coordinates (3 . 3,5 . 2), where the units are meters, what is the distance of the fly from the corner of the room? Correct answer: 6 . 15873 m. Explanation: Given : Δ x = 3 . 3 m and Δ y = 5 . 2 m . Using the Pythagorean Theorem, d = radicalBig (Δ x ) 2 + (Δ y ) 2 = radicalBig (3 . 3 m) 2 + (5 . 2 m) 2 = 6 . 15873 m . 002 (part 1 of 2) 10.0 points Two points in the xy plane have cartesian coordinates ( x 1 , y 1 ) and ( x 2 , y 2 ), where x 1 = 3 . 9 m, y 1 = − 10 m, x 2 = − 10 m, and y 2 = 9 . 2 m. Find the distance between these points. Correct answer: 23 . 7034 m. Explanation: By simple geometry of triangle, the dis- tance between two points is d = radicalBig ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 = { [ − 10 m − (3 . 9 m)] 2 + [9 . 2 m − ( − 10 m)] 2 } 1 / 2 = 23 . 7034 m . 003 (part 2 of 2) 10.0 points What is the angle between the line connecting the two points and x-axis (measured counter- clockwise from the x-axis), within the limits of − 180 ◦ to +180 ◦ )? Correct answer: 125 . 903 ◦ . Explanation: The angle is θ = arctan parenleftbigg y 2 − y 1 x 2 − x 1 parenrightbigg = arctan bracketleftbigg 9 . 2 m − ( − 10 m) − 10 m − (3 . 9 m) bracketrightbigg = 125 . 903 ◦ ....
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Vectors - adamkiewicz(ja28724 – Vectors – Morozova...

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