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6.2.
Model:
The boat is treated as a particle whose motion is governed by constantacceleration kinematic
equations in a plane.
Visualize:
Solve:
Resolving the acceleration into its
x
and
y
components, we obtain
()
( )
22
ˆˆ
0.80 m/s
cos40
0.80 m/s
sin40
ai
=°
+
r
j
°
( ) ( )
0.613 m/s
0.514 m/s
ij
=+
From the velocity equation
,
10
vva
tt
−
rrr
( ) ( )
1
ˆ
5.0 m/s
0.613 m/s
0.514 m/s
6 s
0 s
vi
i
j
+
−
r
( ) ( )
8.68 m/s
3.09 m/s
r
The magnitude and direction of
are
v
8.68 m/s
3.09 m/s
9.21 m/s
v
=+=
1
11
1
3.09 m/s
tan
tan
20
8.68 m/s
y
x
v
v
θ
−−
==
=
°
north of east
Assess:
An increase of speed from 5.0 m/s to 9.21 m/s is reasonable.
6.6.
Model:
The model rocket will be treated as a particle. Kinematic equations in two dimensions apply. Air
resistance is neglected.
Visualize:
The horizontal velocity of the rocket is equal to the speed of the car, which is 3.0 m/s.
Solve:
For the rocket, Newton’s second law along the ydirection is:
net
R
R
FFm
g
m
a
=−=
rr
( )
2
1
8.0 N
0.5 kg
9.8 m/s
0.5 kg
y
a
⇒=
−
2
6.2 m/s
=
Thus using
2
1
10 010
2
yy
yy v tt
a
− +
−
,
2
2
1
1R
2
20 m
0 m
0 m
6.2 m/s
0 s
t
=++
−
( ) ( )
1
20 m
3.1 m/s
t
1
2.54 s
t
Since
t
1
is also the time for the rocket to move horizontally up to the hoop,
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2
1
10 010
1
0
2
xx
x
xvt
t
a
t
t
=+
−+
−
( )( )
0 m
3.0 m/s
2.54 s
0 s
0 m
=
7.62 m
Assess:
In view of the rocket’s horizontal speed of 3.0 m/s and its vertical thrust of 8.0 N, the aboveobtained
value for the horizontal distance is reasonable.
6.11.
Model:
The bullet is treated as a particle and the effect of air resistance on the motion of the bullet is
neglected.
Visualize:
Solve:
(a)
Using
(
2
1
100
10
2
yy
yyvtt
a
tt
− +
−
)
, we obtain
( )
2
22
1
1
2
2.0
10
m
0 m
0 m
9.8 m/s
0 s
t
−
−×
= + +−
−
1
0.0639 s
t
⇒=
(b)
Using
2
1
1
0
2
x
xvtt
a
−
,
( )
0
50 m
0 m
0.0639 s
0 s
0 m
x
v
0
782 m/s
x
v
Assess:
The bullet falls 2 cm during a horizontal displacement of 50 m. This implies a large initial velocity, and a
value of 782 m/s is understandable.
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This note was uploaded on 05/05/2008 for the course PHYS 141 taught by Professor Staff during the Spring '06 term at Cal Poly.
 Spring '06
 staff
 Acceleration

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