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Unformatted text preview: 3.26. Visualize: Solve: (a) θ E = tan −1 ⎛ 1 ⎞ = 45°
⎜⎟
⎝1⎠
2
θ F = tan −1 ⎛ 1 ⎞ = 63.4°
⎜⎟
⎝⎠ Thus φ = 180° − θ E − θ F = 71.6°
(b) From the figure, E = 2 and F = 5. Using G 2 = E 2 + F 2 − 2 EF cos φ = ( 2) 2 + ( 5) 2 − 2( 2)( 5)cos(180° − 71.6°)
⇒ G = 3.00.
sin α sin(180° − 71.6°)
=
⇒ α = 45°
2.975
5
Since θ E = 45° , the angle made by the vector G with the +xaxis is θG = (α + θ E ) = 45° + 45° = 90°.
(c) We have Furthermore, using Ex = +1.0, and E y = +1.0 Fx = −1.0, and Fy = +2.0 Gx = 0.0, and ⇒G = ( 0.0 ) G y = 3.0
2 + ( 3.0 ) = 3.0,
2 and θ = tan −1 G y 
Gx  ⎛ 3.0 ⎞
= tan −1 ⎜
⎟ = 90°
⎝ 0.0 ⎠ That is, the vector G makes an angle of 90° with the xaxis.
Assess: The graphical solution and the vector solution give the same answer within the given significance of
figures. ...
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This note was uploaded on 12/10/2011 for the course PHYS 1211 taught by Professor Geller during the Fall '09 term at University of Georgia Athens.
 Fall '09
 geller

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