PHY2053 RECITATIONS, SPRING 2011
Recitation 4
(Chapter 3, 4) Feb 7  11
Ch. 3 # 42.
In the javelin throw at a trackandfield event, the javelin is launched at a speed of 29 m/s at
an angle of 36° above the horizontal. As the javelin travels upward, its velocity points above the horizontal at
an angle that decreases as time passes. How much time is required for the angle to be reduced from 36° at
launch to 18°?
42.
REASONING
As shown in the drawing, the angle
that the velocity vector makes with the horizontal is
given by
tan
y
x
v
v
θ
=
where, from Equation 3.3b,
0
0
0
sin
y
y
y
y
v
v
a t
v
a t
=
+
=
+
x
y
v
y
v
x
v
and, from Equation 3.3a (since
a
x
= 0 m/s
2
),
0
0
0
cos
x
x
v
v
v
=
=
Therefore,
0
0
0
0
sin
tan
cos
y
y
x
v
v
a t
v
v
+
=
=
SOLUTION
Solving for
t
, we find
(
29
(
29
(
29
0
0
0
2
cos
tan
– sin
29 m/s
cos 36 tan 18 – sin 36
0.96 s
–9.80 m/s
y
v
t
a
°
°
°
=
=
=
____________________________________________________________________________________________
Ch. 3 # 78.
Two boats are heading away from shore. Boat 1 heads due north at a speed of 3.00 m/s
relative to the shore. Relative to boat 1, boat 2 is moving 30.0° north of east at a speed of 1.60 m/s. A
passenger on boat 2 walks due east across the deck at a speed of 1.20 m/s relative to boat 2. What is the
speed of the passenger relative to the shore?
78.
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 Spring '09
 Staff
 Pythagorean Theorem, Acceleration, Force, m/s, net force

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