2.48. CHAPTER 2, PROBLEM 48
153
2.48
Chapter 2, Problem 48
Problem:
On a peaceful lake, Boat A has velocity
V
a
i
. For a Boat A observer, Boat B appears to have
a velocity
V
b
j
. Boat B launches a missile with relative velocity
−
1
2
V
a
i
−
V
b
j
+
v
k
. The unit vectors
i
and
j
are parallel to the lake surface, and
k
points vertically upward. The missile lands on Boat A
and displays a banner that says “BOOM.” Determine the original distance between the boats,
L
,asa
function of
V
a
,
v
, and the acceleration of gravity,
g
.
Solution:
We know that the absolute velocity of Boat A is
v
a
=
V
a
i
We are also given the velocity of Boat B relative to Boat A, which is
v
b/a
=
V
b
j
Finally, the velocity of the missile relative to Boat B is
v
m/b
=
−
1
2
V
a
i
−
V
b
j
+
v
k
Thus, the absolute velocity of Boat B is
v
b
=
v
a
+
v
b/a
=
V
a
i
+
V
b
j
and the absolute velocity of the missile is
v
m
=
v
b
+
v
m/b
=
V
a
i
+
V
b
j
−
1
2
V
a
i
−
V
b
j
+
v
k
Therefore, the absolute velocity of the missile is
v
m
=
1
2
V
a
i
+
v
k
Focusing first on the missile, it moves under the influence of gravity. This means the missile experiences
acceleration equal to
−
g
k
. Hence, its position vector,
r
m
,isg
ivenby
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 Spring '06
 Shiflett
 Acceleration, Velocity, 2 g, Missile

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