Homework 1 – Solution
CHANG
1 To find the
x
−
y
components of a vector, we first use the vector as the diagonal
to sketch a rectangular box with its sides parallel to the coordinate axes. Then we can break up
the vector graphically to identify the components, and note that the directions of the
components have to match that of the vector. Specify the signs corresponding to the directions
of the components, and calculate their magnitudes using sine (opposite side) or cosine
(adjacent) functions based on the triangles. Alternatively we can directly use the formulas,
V
x
V
cos
and
V
y
V
sin
, and note the angle
must be measured from the
x
-axis that is
laced at the tail of the vector. The angle
is positive (negative) for counterclockwise
(clockwise) rotation.
−
Acceleration vector
a
respect to
x
1
−
y
1
coordinates: From the figure shown we get
O
a
= 5 m/s
2
x
1
y
1
30°
θ
a
1
a
x
1
a
y
1
a
x
1
a
sin30
∘
5sin30
∘
2.50 m/s
2
a
y
1
a
cos30
∘
5cos30
∘
4.33 m/s
2
Or use
a
1
60
∘
a
x
1
5cos60
∘
2.50 m/s
2
a
y
1
5sin60
∘
4.33 m/s
2
−
Acceleration vector
a
respect to
x
2
−
y
2
coordinates: From the figure shown we get

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