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angle is –37.5°, which is to say that it is 37.5°
clockwise
from the +
x
axis. This is
equivalent to 322.5° counterclockwise from +
x
.
(c) We find
ˆˆ
ˆ
ˆ
[43.3 ( 48.3) 35.4] i [25 ( 12.9) ( 35.4)] j
(127 i
2.60 j) m
abc
−+=
−−
+
− −−
+−
=
+
G
GG
in unitvector notation. The magnitude of this result is
22
2


(127 m)
(2.6 m)
1.30 10 m.
−+ =
+
≈
×
G
(d) The angle between the vector described in part (c) and the +
x
axis is
1
tan (2.6 m/127 m) 1.2
−
≈°
.
(e) Using unitvector notation,
G
d
is given by
(4
0
.
4
i 4
7
.
4
j
)
m
dabc
=+−=−
+
,
which has a magnitude of
( 40.4 m)
(47.4 m)
62 m.
−+
=
(f) The two possibilities presented by a simple calculation for the angle between the
vector described in part (e) and the +
x
axis are
1
tan (47.4/( 40.4))
50.0
−
−=
−
°
, and
180
( 50.0 ) 130
°+ −
° =
°
. We choose the latter possibility as the correct one since it
indicates that
G
d
is in the second quadrant (indicated by the signs of its components).
19. Many of the operations are done efficiently on most modern graphical calculators
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This note was uploaded on 05/17/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.
 Spring '08
 Any
 Physics

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