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PHYS 0212 BallisticMotion
1
Bench Top
Ballistic
Launcher
Impact
Point
Start
Point
Launch
Point
Plumb
Bob
A
1
h
2
h
Impact Distance
h
1
= Height of the center of mass above the launch point
h
2
= Height of the launch point above the table
Ballistic Motion
PHYS 0212 BallisticMotion
2
The basic procedure:
3. Measure the impact distance as a function of height
h
2
.
1. Repeatedly measure the impact distance
for a fixed height
h
2
.
A
2. Calculate the mean and standard deviation of the impact distance
.
A
4. Plot
versus
h
2
.
2
A
We can find the impact distance of the ball if we know its velocity at the launch
point.
Horizontal (
x
) and vertical (
y
) motions are independent, so we can write out the
equations of motion for constant acceleration.
x
direction
y
direction
2
1
00
2
xx
xxv
t a
t
=+ +
2
1
2
yy
y
yv
t
0
0
0
0
0
x
x
x
vv
a
=
=
=
02
0
0
y
y
y
h
ag
v
=
=
= −
At the launch point
(
assuming the initial
velocity is completely
horizontal
)
}{
PHYS 0212 BallisticMotion
3
x
direction
y
direction
()
2
1
2
2
1
0
2
t
x
vt
t
=+
+
2
1
2
2
1
2
2
0
yyv
t
y
htg
t
=+ +−
0
x
=
2
1
2
2
y
hg
t
=−
Bench Top
A
Impact Distance
2
h
When the ball reaches the impact point:
and
0
xy
==
A
0
=
A
2
1
2
2
0
t
The time
t
is the same in
both of these equations.
0
v
PHYS 0212 BallisticMotion
4
0
2
2
2
0
t
v
t
v
=
=
A
A
2
1
2
2
2
0
v
=
A
0
=
A
2
1
2
2
0
t
Eliminate
t
from both equations:
22
2
0
2
h
v
g
=
A
Solve for
2
A
2
1
2
2
t
=
Okay, so how do we determine the initial velocity
v
0
?
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 Spring '08
 Naples
 Physics, Center Of Mass, Mass

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