determine the relationship
between distance the ball
travelled horizontally and
the height of the start point
15 October 2012
Done by China Suetni 12i
An experiment to determine the relationship between distance
the ball travelled horizontally and the height of the start point
 Research question
The aim of the experiment is to determine the distance the ball travelled due to the height.
 Hypothesis
The ski jump player starts descending from quite high position to jump for longer distance. Therefore
I hypothesised that the distance the ball travelled would be proportional to the height.
 Variables

Independent variable [height of the start point]
Height was measured by my partner by using metre ruler at 90°

Dependent variable [distance the ball travelled horizontally]
The horizontal distance was taken by using same metre ruler used to measure the height

Control variables [use of same ball, plate to be made the slope, retort stand, metre rulers, digital
stopwatch, / keep same surroundings, / and same person to measure the height and the distance]

Use of same tools

Same ball must be used as the surface are of the ball relates to the friction that the ball
makes when the ball roll down and which changes the initial velocity. Also the size of
the ball changes to the air residence the ball get when the ball is dropping.

Same plate or the slope must be used as again the changes of the surface area relates to
the friction which changes the initial velocity.


Same retort stand must be used and make sure that it does not move when the ball roll.

Same metre ruler must be used to keep the measuring scale exactly same.

Same digital stopwatch must be used for same sensitivity of the stopwatch
Keep same surroundings

Although the surroundings do not affect the result very much for this experiment, it is
better to be done in same surroundings like in same place and on the same day as they
make very small change of gravity and some other factors.

Same person for measuring

Depends on person measuring skill might change. To get more accurate result all the
measurements were taken by same person in the experiment.

For more accuracy….

Clamp is used then the plate was fixed strongly

Sand is placed to make sure the place the ball dropped and distance to be measured.

Check that the table is horizontal if the experiment is made on the table.

The height of the table must be same as the distance would change.

The metre ruler is stacked with ‘TACK-IT’ to make sure that the rulers are not moving.

We stacked two metre rulers and used the other metre ruler to make sure that both
rulers have same value (to check the ruler to see is put sprightly)
 Apparatus

Iron ball

Retort stand

Plate

Sand

Clamps

Metre rulers (smallest scale - 0.100cm, accuracy ±0.050cm)

Digital stopwatch (smallest number – 0.010seconds, accuracy ±0.010seconds)
 Diagram
h = vertical height for the ball to be
ux
h
dropped.
sy
uy
ux = initial horizontal velocity.
ay
uy = initial vertical velocity.
ay = initial vertical acceleration.
sx = horizontal distance.
sx
Put
sy sand
= vertical distance.
 Methods
1.
Check the tools that these tools work properly.
2.
Set the apparatus like the diagram above. Put sand. Fix the stick tools strongly and make sure
that tools are not moving except iron ball during the experiment.
3.
Measure the first height to the table
4.
Measure the distance the ball travelled. Repeat 5 times.
5.
Change the start point to lower and repeat method number 3 and 4.
6.
Take data for 5 different heights.
 Data collection

Constant uncertainty
Height and distance travel
The smallest scale that the metre ruler can measure is 0.1cm so the uncertainty is
0.1 / 2=±0.05cm

Raw data
Experiment
number
Height of the start point
Horizontal distance the ball travelled (s) /cm / ±0.05cm
on the table
(h) /cm / ±0.05cm
1
2
3
4
5
1
22.8
54.4
52.9
51.3
53.5
54.6
2
20.0
53.6
50.1
52.6
51.1
50.1
3
17.0
49.1
49.9
48.6
48.1
48.3
4
14.0
46.1
43.7
44.9
44.6
45.9
5
11.0
43.3
43.8
42.8
42.5
41.6
6
8.0
34.4
34.2
35.4
36.3
34.4
Processed data

Final velocity = 0, acceleration (gravity) = 9.8m𝑠 −1
Experiment
Height of the
start point on
the table
Average
Initial velocity (v) / m s⁻¹
3
Uncertainty
2
2.63
Average
1
2.59
2.90
distance the
2.60
2.93
2.97
for distance
0.35
2.91
2.93
3.09
distance the
1.05
0.43
3.01
3.13
3.21
ball advanced
34.90
1.10
0.45
3.10
3.13
3.17
the ball
8.0
42.80
1.20
0.49
3.24
3.22
ball advanced
1
11.0
45.00
0.90
0.52
3.27
(S) / m
2
14.0
48.80
1.75
0.53
advanced
3
17.0
51.50
1.65
(S) / cm
4
20.0
53.30
number
(h) /cm /
5
22.8
±0.05cm
6
4
2.60
5
2.90
2.62
Average
0.04
0.04
0.04
𝑆𝑢𝑚 𝑜𝑓 𝑡ℎ𝑒 𝑟𝑒𝑠𝑢𝑙𝑡 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑡ℎ𝑒 𝑡𝑟𝑎𝑖𝑙𝑠
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑟𝑖𝑎𝑙𝑠
(34.4+34.2+35.4+36,3+34.4)
5
= 34.90 cm (2 decimal places)
Repeat the calculation for other tests
Uncertainty of distance the ball advanced

𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 − 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
2
36.3−34.2
2
= 1.05 (2 decimal places)
Repeat the calculation for other tests

Average distance the ball advanced (S) m
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡ℎ𝑒 𝑏𝑎𝑙𝑙 𝑎𝑑𝑣𝑎𝑛𝑐𝑒𝑑 (𝑆) 𝑐𝑚
100
34.9
100
= 0.35 m (2 decimal places)
Repeat the calculation for other tests

Initial velocity (v) m s⁻²
Uncertainty
2.67
2.86
2.97
Average distance the ball advanced (S) cm

for initial
2.89
3.00
Calculations ( for experiment 1)
velocity
2.97
0.03
0.05
0.05
3.09
3.18
3.23
3.08
3.13
3.27
3.07
3.16
3.24

𝑣 2 = 𝑢2 + 2𝑎𝑠 v=0, a=9.8,
√2 × 9.8 × 0.51=2.60 (experiment 1, trail 1, 2 decimal places)
Repeat the calculation for other tests
Average initial velocity

𝑠𝑢𝑚 𝑜𝑓 𝑡ℎ𝑒 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑟𝑎𝑖𝑙𝑠
2.60+2.59+2.63+2.67+2.60
5
= 2.62 m/s² (2 decimal places)
Repeat the calculation for other tests
Uncertainty of initial velocity

𝑚𝑎𝑥𝑖𝑚𝑢𝑛 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 − 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
2
2.67−2.59
2
= 0.04 (2 decimal places)
Repeat the calculation for other tests
 Graph
 Average distance due to height
 Average initial velocity due to height
 Conclusion
My research question was to determine the distance the ball travelled due to the height.
Although the line on the graph for average distance due to height does not straight, the
distance gets longer as the height increase.
The first graph (average distance due to height) shows average distance and height is
proportional and that was what I hypothesised.
Also the second graph (average initial velocity due to height) proves that as height
increase, the initial velocity increases.
The best fit line is out of the uncertainty for 1st and 2nd points. Also the line is not within
the maximum line and minimum line. The possible reason for it is we did not get the
hang of measuring or releasing the ball.
Both graph supposed to pass through the original line as if the height is 0cm, there is no
force towards, and so the distance and initial velocity should be 0.
The biggest error for this experiment is that the curve of the plate was too big which was
more than 90°in some part of the plate.
h
Z
 As h (height) increases,
ux
sy
uy
ay
Sx (distance) increases
 As h increase, initial
velocity when the ball
is point Z, increases
sx
 Errors and improvements

Possible system errors
System errors
How do the errors affect the
experiment
Improvements
When the curve is more than 90°,
The curve of the
plate was more
than 90°
Use of sand which
easily move when
the impacts of the
ball when it
bounced.
The ball does not
roll and drop
straightly.

the ball might drop rather than roll
on the plate. As a result, the ball
lost its acceleration when it drop
and hit the plate, and the initial
velocity will change.
The trace of the ball when it
dropped might be disappeared by
the impact of the ball bounced.
We fixed the ruler first, so the
distance is different when the ball
rolled straightly and when the ball
did not roll straightly. The distance
must be longer when the ball land
right side or left side.
Make the plate gentle. Then the
ball would not drop and lost its
acceleration.
Use of something sticky and not
move easily such as clay. Then
the ball would be stuck on the
place where the ball dropped
and which does not move easily.
Make a small wall in the plate
to make sure that the ball rolls
straightly.
Possible random errors
Random errors
How do the errors affect the experiment
The ball might gain force by the person
My partner released
when I he pushes the ball to any
the ball
direction. If the initial velocity is not 0,
all the calculations should be changed.
Improvements
Use of data loggers with sensors. It
gives us the initial velocity and final
velocity if these gates are located start
point and goal point, and release the
ball several cm away from start point.
We might relocate the instruments
We did the experiment
several mm further or nearer. That
Finish the experiment at one time or
in 2 days
causes the measurement would be
mark the position of the instruments.
changed.