Lesson 1.3 Homework Solutions
1.
A bear walks northeast for 12 m and then east for 12 m. Show each
displacement graphically and find the resultant displacement vector.
12 m Northeast vector can be written as 12 cos 45
i
+ 12 sin 45
j
=
8
.
5
i
+ 8.5
j
12 m East vector = 12
i
The resultant of these vectors = 8.5
i
+ 8.5
j
+ 12
i
=
20.5
i
+ 8.5
j
The magnitude of the resultant =
22
20.5
8.5
22.2
m
+=
The angle
θ
the resultant makes with the positive x axis is given by
8.5
tan
0.41
20.5
y
x
θ
==
=
.
Therefore,
θ
= tan
1
0.41 =
22.3
o
.
1
2
m
n
o
r
t
h

e
a
s
12 m east
.
22.3
o
2.
Find the rectangular components of a vector v that has a magnitude of
12 ms
1
and is oriented at an angle 37
o
with the positive xaxis.
xcomponent = 12 cos 37
o
=
9.6 m.s
1
ycomponent = 12 sin 37
o
=
7.2 m.s
1
3.
A vector A has an xcomponent 4.5 m and a ycomponent 2.2 m.
What is the magnitude and direction of vector A?
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View Full DocumentThe magnitude of vector A is:
22
4.5
2.
50
2
.
N
A
=+
=
The angle
θ
vector makes
with the xaxis is:
1
2.2
tan
26
4.5
154
26 180
o
o
θ
−
==
−
−
=
=
−+
154
o
2.2 m
4.5 m
A
4.
Find the resultant of the following vectors:
30
o
o
45
o
20 N
15N
25 N
B
C
The three vectors can be written in component form as:
A = 20 cos 45
o
i
+ 20 sin 45
o
j
=
14.14
i
+ 14.14
j
B = 25 cos 150
o
i
+ 25 sin 150
o
j
=
21.65
i
+ 12.5
j
C = 15 cos 300
o
i
+ 15 sin 300
o
j
= 7.5
i
– 12.99
j
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 Fall '10
 George
 Physics, Acceleration, Work, Displacement, tan θ

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