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Homework No. 1
O
a
= 5 m/s
2
υ
= 20 m/s
x
1
y
1
x
2
y
2
50°
30°
20°
Vector components
CHANG
1
A boat is traveling along a
curved path, and when it reaches point
O
the acceleration of the boat
a
and the
velocity of the wind
G
υ
G
are shown in the
figure. Find the components of both vectors
with respect to
x
1

y
1
as well as
x
2

y
2
coordinate systems.
Ans
:
a
x
1
= 2.5 m/s
2
,
a
y
1
= 4.33 m/s
2
;
a
x
2
=
−
3.83 m/s
2
,
a
y
2
=
−
3.21 m/s
2
;
υ
x
1
=
15.3 m/s,
υ
y
1
=
−
12.9 m/s;
υ
x
2
=
−
10 m/s,
υ
y
2
= 17.3 m/s
O
A
= 500 N
B
= 200 N
x
1
y
1
x
2
y
2
75°
35°
25°
CHANG
2
Two tug boats
A
and
B
guiding a
ship at point
O
exert forces on the ship shown
in the figure. Find the components of both
force vectors with respect to
x
1

y
1
as well as
x
2

y
2
coordinate systems.
Ans
:
A
x
1
= 211 N,
A
y
1
=
−
453 N;
A
x
2
= 433
N,
A
y
2
=
−
250 N;
B
B
x
1
= 51.8 N,
B
y
1
B
= 193 N;
B
B
x
2
=
−
68.4 N,
B
y
2
B
= 188 N
Y&F
1.40
Ans
: (a) 10.0 cm, 149
°
(b) 10.0 m,
−
166
°
(or 194
°
) (c) 8.21 km,
−
19.2
°
(or 341
°
)
Vector addition by the components method
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This note was uploaded on 03/04/2009 for the course PHYS 2305 taught by Professor Tschang during the Spring '08 term at Virginia Tech.
 Spring '08
 TSChang
 Physics, Acceleration, Work

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