Projectile Motion
Objective
We are determining the initial velocity of a
launched ball by measuring how far it travels horizontally
before impacting the floor. With this velocity, we will be
able to predict the range of the projectile when it is fired
at any angle, and predict the required angle for any range.
Exercise 1: Mathematical Preliminaries
To calculate the initial velocity, we must have a derived mathematical relationship
between the distance traveled and the initial velocity that factor out time. We have two
equations for this:
t
v
R
0
=
and
2
2
1
0
gt
h

=
. Combined we can derive:
0
0
v
R
t
t
v
R
=
⇒
=
h
g
R
v
h
gR
v
v
gR
h
v
R
g
h
gt
h
2
2
2
2
1
2
1
0
0
2
2
0
2
0
2
2
0
2
=
⇒
=
⇒
=
⇒

=

=
To calculate the deviation for the velocity, we must use a different equation than
the standard deviation equation:
( 29
∑
∆
+
∆
=
∆
=
∆
n
i
i
h
h
v
R
R
v
x
R
v
v
2
2
2
2
2
2
0
0
0
0
Exercise 2: Determining the Initial Speed of the
Projectile
Procedure:
We set the launcher to fire horizontally and loaded the ball into the desired launch
distance. After firing, we observed the location of impact with the ground and placed the
carbon paper on the spot. Then we fired four more rounds onto the paper and found the
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 Fall '06
 Cerruti
 Physics, Standard Deviation, Projectile Motion, Velocity, 1 g, 1.68m, 1.6%, 1.659m

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