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Vertical motion
Vertical launching of a light ball
Next, we consider a plastic ball,
made of a thin plastic surface and filled with air
and with a mass of 0.35 kg,
which is thrown upward into the air with
the same initial speed of 20 m/s,
equivalent to 72 km/h, as the metal ball in the previous example.
Below you find some measurements about its height,
after it has been launched
and above the position where it is launched,
at instants of time which differ
0.1 seconds.
|
time (s)
|
0.0
|
0.1
|
0.2
|
0.3
|
0.4
|
0.5
|
0.6
|
0.7
|
0.8
|
0.9
|
|
height (m)
|
0.0
|
1.90
|
3.62
|
5.18
|
6.58
|
7.84
|
8.96
|
9.96
|
10.84
|
11.60
|
| |
|
|
|
|
|
|
|
|
|
|
|
time (s)
|
1.0
|
1.1
|
1.2
|
1.3
|
1.4
|
1.5
|
1.6
|
1.7
|
1.8
|
1.9
|
|
height (m)
|
12.25
|
12.79
|
13.23
|
13.57
|
13.81
|
13.94
|
13.98
|
13.93
|
13.77
|
13.52
|
| |
|
|
|
|
|
|
|
|
|
|
|
time (s)
|
2.0
|
2.1
|
2.2
|
2.3
|
2.4
|
2.5
|
2.6
|
2.7
|
2.8
|
2.9
|
|
height (m)
|
13.17
|
12.73
|
12.19
|
11.57
|
10.86
|
10.07
|
9.19
|
8.24
|
7.22
|
6.12
|
| |
|
|
|
|
|
|
|
|
|
|
|
time (s)
|
3.0
|
3.1
|
3.2
|
3.3
|
3.382
|
|
|
|
|
|
|
height (m)
|
4.96
|
3.74
|
2.46
|
1.13
|
0.0
|
|
|
|
|
|
A graphical representation for the table can be found
here
We can make some initial observations.
1. We find that the plastic ball is a shorter interval of time in the air
then the metal ball,
3,38 s
versus 4,08 s.
2. The maximum height of almost 14 metres
is also substantially smaller than the corresponding
over 20 metres of the metal ball.
Hence, it is clear that the motion of the plastic ball
is different from the motion of a freely falling object.
Its equation of motion cannot be the same
as that for the solid metal ball, i.e.
a ≠ - g
In the following we study its acceleration.
average velocity