HW#2b part 2
Page 1 of 3
8.
9.
10. Practice with vectors: (important!)
For each of the vectors below,
I.) do a rough sketch of it
II.) convert it to the form it is not already in (size&direction, or components)
(Note: cw=clockwise, ccw=counterclockwise)
a.)
= 5 m, 30o ccw from +x axis
Dx =
m
Dy =
m
y
r
A
θ
Ay
x
Ax
HW#2b part 2
Page 2 of 3
Answers. Here and later we will use the relations between the (magnitude, angle) and
component representations of a vector:
A = Ax2 + Ay2 ⎫
⎪ ⎧ Ax = A cos θ
Ay ⎬ ⎨ A = A sin θ
tan θ =
⎪ ⎩ y
Ax ⎭
So for part (a),
y
Dx = D cos θ = ( 5 m ) cos 30° = 4.33 m
D y = D sin θ = ( 5 m ) sin 30° = 2.5 m
5m
Ay
30 °
x
Ax
b.)
= 15 m/s, 10o cw from –y axis
vav x = -2.604 m/s
vav y = -14.77 m/s
θ=260 °
y
Ax
Answer. Look at the diagram - the angle, measured
in the usual direction from the positive x axis, is equal
to 260 °. And both x and y components of the vector
are negative. Let's see if the trig functions get this
right automatically.
Ay
x
15 m/s
10 °
Ax = A cos θ = (15 m/s ) cos 260° = −2.604 m/s
Ay = A sin θ = (15 m/s ) sin 260° = −14.77 m/s
c.) Qx = -6 m, Qy = +2 m
y
= 6.325m, 18.43 o cw from –x axis
Answer. Here we make the transformation
back from components to magnitude and
angle.
( −6 m ) + ( 2 m )
2
180°-θ
Qx
-6 m
Q = Qx2 + Qy2
=
θ
Qy
2m
x
2
= 6.325 m
tan θ =
Qy
Qx
=
( 2 m ) = −.33333
( −6 m )
θ = −18.43 + 180 = 161.57°
The angle called for is not the usual angle θ, but is equal to 180° minus the standard
angle. So the answer is 180°-161.57° = 18.43°.
HW#2b part 2
Page 3 of 3
11. Use unit vector notation to express each of the vectors in Figure 3-39, in which the
magnitudes of A, B, C, and D are respectively given by 36 m, 48 m, 24 m, and 36 m.
A =( 27.6 x + 23.1 y) m
B =( 45.4 x + (-15.6) y) m
C =( -21.8 x + 10.1 y) m
D =( 36 x + 0 y) m
Notice that here A, B, C and D and also x and y are bold, meaning they are vectors.
Ax= A*cos (40) = 27.6
Ay=A*sin(40) = 23.1
Bx= B*cos (19) = 45.4
By= - B*sin(19) = -15.6
Cx= - C*cos (25) = - 21.8
Cy= C *sin(25) = 10.1
Dx= D*cos (90) = 0
Dy= D*sin(90) = D = 36
THESE ARE EXTREMELY IMPORTANT.
PLEASE PRACTICE AGAIN AND AGAIN.