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117. The (box)car has velocity
G
vv
cg
i
=
1
#
relative to the ground, and the bullet has
velocity
G
v
bg
02
2
i
j
=+
cos
#
sin
#
θθ
relative to the ground before entering the car (we are neglecting the effects of gravity on
the bullet).
While in the car, its velocity relative to the outside ground is
G
v
bg
08
2
.c
o
s
#
#
i
0.8
j
2
(due to the 20% reduction mentioned in the problem). The
problem indicates that the velocity of the bullet in the car
relative to the car
is (with
v
3
unspecified)
G
bc
j
=
3
#
. Now, Eq. 444 provides the condition
22
3
1
ˆˆ
ˆ
ˆ
0.8
cos i 0.8
sin
j
j
i
v
v
v
+=
+
GG
G
so that equating
x
components allows us to find
θ
. If one wished to find
v
3
one could also
equate the
y
components, and from this, if the car width were given, one could find the
time spent by the bullet in the car, but this information is not asked for (which is why the
width is irrelevant). Therefore, examining the
x
components in SI units leads to
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 Spring '08
 Any
 Physics, Gravity

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