h7 - hernandez (ejh742) – homework 07 – Turner –...

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Unformatted text preview: hernandez (ejh742) – homework 07 – Turner – (58120) 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 (part 1 of 2) 10.0 points A particle undergoes three displacements. The first has a magnitude of 15 m and makes an angle of 28 ◦ with the positive x axis. The second has a magnitude of 8 . 7 m and makes an angle of 138 ◦ with the positive x axis. (see the figure below). After the third displacement the particle returns to its initial position. 138 ◦ 28 ◦ 1 5 m 8 . 7 m Find the magnitude of the third displace- ment. Correct answer: 14 . 5404 m. Explanation: Given : bardbl vector A bardbl = 15 m , θ a = 28 ◦ , bardbl vector B bardbl = 8 . 7 m , and θ B = 138 ◦ . θ C θ A θ B A B C − C Since vector A + vector B + vector C = 0 , we have vector C = − vector A − vector B . The components of the third displacement vector C are C x = − A x − B x = − A cos θ A − B cos θ b = − (15 m) cos28 ◦ − (8 . 7 m) cos138 ◦ = − (13 . 2442 m) − ( − 6 . 46536 m) = − 6 . 77885 m and C y = − A y − B x = − A sin θ A − B sin θ b = − (15 m) sin28 ◦ − (8 . 7 m) sin138 ◦ = − (7 . 04207 m) − (5 . 82144 m) = − 12 . 8635 m . The magnitude of vector C is bardbl vector C bardbl = radicalBig C 2 x + C 2 y = radicalBig ( − 6 . 77885 m) 2 + ( − 12 . 8635 m) 2 = 14 . 5404 m . 002 (part 2 of 2) 10.0 points Find the angle of the third displacement (mea- sured from the positive x axis, with counter- clockwise positive within the limits of − 180 ◦ to +180 ◦ ). hernandez (ejh742) – homework 07 – Turner – (58120) 2 Correct answer: − 117 . 788 ◦ . Explanation: tan θ C = C y C x θ C = arctan bracketleftbigg C y C x bracketrightbigg = arctan bracketleftbigg ( − 12 . 8635 m) ( − 6 . 77885 m) bracketrightbigg = − 117 . 788 ◦ ....
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This note was uploaded on 06/14/2011 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas.

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h7 - hernandez (ejh742) – homework 07 – Turner –...

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