Physics 2 Tutorial 5: Vectors
By Calvin Patel
1. Given that vector
~
A
= (
√
5
,
56
◦
)
,
~
B
= (

4
,
1)
,
~
C
= (1
,

2)
,
and
~
D
= (
√
10
,
252
◦
), compute the following
and present a graphical representation of the resultant vector in terms of the original vectors.
(a)
~
D
+
~
A
(b)
~
B

~
D
(c)
~
A
+
~
D
+
~
B
(d)
~
C

~
A
+
~
B
2. Convert the following vectors from cartesian to polar or from polar to cartesian coordinates.
(a) (

2
,
3)
(b) (

10
,

2)
(c) (5
,
105
◦
)
(d) (3
,
250
◦
)
3. Compute the following vector sums taking
~
A
= (3
,
2)
,
~
B
= (1
,

4 and
~
C
= (5
,.
2). Note that some of
the vectors are multiplied by a scalar quantity. Graph the vectors.
(a)
~
A
+
~
B

2
~
C
(b) 3
~
A

2
~
B

2
~
C
(c)

1
2
~
A

2
~
B

3
~
C
(d) 2
~
A
+ 2
~
B
+ 3
~
C
4. You are an explorer and after you land on shore you head east for 3 miles and north for 2 miles and
set up camp. Take
ˆ
i
as East and
ˆ
j
as North.
(a) What is your position vector?
(b) You are standed because you broke you leg, however you have a treasure map that says the
treasure is 2 miles to the west of your location (the camp). You take our your cell phone and call
your girlfriend to go get that treasure. If she is 4 miles south and 3 miles east of your location,
what is the vector from her position to the treasure.
(c) You suddenly get better and ﬁnd a tower by traveling 5 miles 30
◦
North of East, what is the
vector from you to your landing site?
5. Out at sea you and your friend are lost at sea and want to ﬁnd one another. You see a lightower at
(0
,
500) meters and your friend sees the same tower at (

300
ˆ
i
+ 100
ˆ
j
) meters from his position.
(a) Find the vector of his position from your position in cartesian coordinates.
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 Fall '10
 ManojKaplinghat
 Physics, Cartesian Coordinate System, Polar coordinate system, 2 miles

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