Quiz5Solutions - Physics 2: Quiz 5 Solutions November 4,...

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Physics 2: Quiz 5 Solutions November 4, 2010 1. Vector -→ A has length 4 and a polar angle of 140 degrees, vector B =3 ˆ i +2 ˆ j , and vector C has length 2 and a polar angle of 30 degrees. Find: a) the x component of C - A We need to start by getting vectors A and C into Cartesian coordinates which will allow us to take the diference. We can use the Formula: ( r, θ ) ( r cos θ, r sin θ ) to convert From polar to Cartesian coordinates. ±or A we have: A = (4 , 140 ) = (4 cos 140 , 4 sin 140 ) =( - 3 . 57 , 2 . 57) = - 3 . 57 ˆ i . 57 ˆ j C we have: C = (2 , 30 ) = (2 cos 30 , 2 sin 30 ) = ± 3 , 1 ² = 3 ˆ i + ˆ j ±or the x component oF the diference between the vectors, we just take the diference between the x components oF each vector: ± C - A ² x = C x - A x = 3 - ( - 3 . 57) =5 . 3 b) the magnitude of 2 B - 3 ˆ i To get the magnitude we will need both the x and y components oF the diference. We have: 2 B - 3 ˆ i =2 ± 3 ˆ i ˆ j ² - 3 ˆ i =6 ˆ i +4 ˆ j - 3 ˆ i ˆ i ˆ j so the magnitude is given by: 1
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± ± ± 2 -→ B - 3 ˆ i ± ± ± = ± ± ± 3 ˆ i +4 ˆ j ± ± ± = ² 3 2 2 =5 c) the polar angle of A - B +2 C We can get the polar angle from the Cartesian components. We have: A - B C = ³ - 3 . 57 ˆ i . 57 ˆ j ´ - ³ 3 ˆ i ˆ j ´ ³ 3 ˆ i + ˆ j ´ = - 3 . 57 ˆ i - 3 ˆ i 3 ˆ i . 57 ˆ j - 2 ˆ j ˆ j = - 3 . 11 ˆ i . 57 ˆ j And we know that, since the vector is in the second quadrant: θ = arctan ³ y x ´ + 180 = arctan µ 2 . 57 - 3 . 11 + 180 = - 39 . 6 + 180 = 140 2. Elizabeth and Kelsey do the following experiment to Fgure out the height of a building.
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This note was uploaded on 11/21/2010 for the course PHYSICS Physics 2 taught by Professor Manojkaplinghat during the Fall '10 term at UC Irvine.

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Quiz5Solutions - Physics 2: Quiz 5 Solutions November 4,...

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