fisica1-youn-e-freedman-exercicios-resolvidos

1.68:a) R = A + B + C
x
R
y
=
x
x
x
o o
o
o o
( 12.0 m) cos ( 90 − 37 ) + ( 15.00 m) cos( − 40 ) + ( 6.0 m) cos( 180 + 60 )
= 15.7 m, and
= A
=
y
+ B
y
+ C
y
o o
o
o o
( 12.0 m) sin ( 90 − 37 ) + ( 15.00 m) sin( − 40 ) + ( 6.0 m) sin( 180 + 60 )
= −5.3 m.
The magnitude of the resultant is R
2 2
= R x
+ Ry
= 16.6 m , and the direction from
− 5.3
o
the positive x-axis is arctan ( ) = −18.6
15.7
. Keeping extra significant figures in the
intermediate calculations gives an angle of − 18 .49°,
which when considered as a
positive counterclockwise angle from the positive x-axis and rounded to the
o
nearest degree is 342 .
b)
S
S
x
y
= −3.00 m − 7.22 m −11.49 m = −21.71m;
= −5.20 m −
⎡ ( −5.14)
⎤
θ = arctan ⎢ = 13.3
( 21.71)
⎥
⎣ − ⎦
S =
( −21.71 m)
( − 9.64 m) − 9.58 m = −5.14
m;
2
+ ( −5.14
m)
o
2
= 22.3 m