Physics 1 – Projectile Motion
PROJECTILE motion
Aims
 To study projectile motion.
 To analyse experimental data using Excel.
In this experimental tutorial you will first undertake a tutorial question to predict the
motion of a ball bearing launched from a track and then set up an experiment to test
this prediction.
Part 1: Tutorial Question (15 mins)
Track
h
v
Catcher
Light gates
y
Landing pad + mouse mat
d
Figure 1: Schematic of experiment.

If a ball of mass m is placed at the start position on the track shown in
Figure 1.1, and allowed to roll along the track, falling a distance h
vertically, what is its change in Potential Energy?
1.1
Find an expression for its Kinetic Energy and its velocity at the time it leaves
the track.
1.2
The end of the track is set along the horizontal. Find an expression for how
long the ball takes to hit the landing pad a distance y below the launch point.
1.3
Find an expression for how far horizontally from the launch point it travels.
Write your answer in terms of y and h.
Part 2: Excel Spreadsheet (10 mins)
 Open a new spreadsheet for the analysis of this experiment. You will make
predictions based on theory and from practical work so it is wise to consider how
your spreadsheet will be laid out.
 In one column, put your formula to predict the velocity based on the height
difference between release point and launch point. Start, for example, with 20 cm.
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Physics 1 – Projectile Motion
 Now measure the depth, y , from the launch point to the landing pad.
2.1
2.2
Predict the time of flight.
Predict the horizontal distance travelled after launch.
 In another column of your spreadsheet, add the formula to calculate velocity based
on the time taken to travel the distance between the two light gates, 20 mm.
Hint: Put all variable numbers in their own cells in Excel.
Do not perform the calculations yourself – enter the equations into excel and
get excel to perform the calculations.
Here is an example layout:
Release
Height
(m)
0.1
Apparatus
Light
Gate 1
Light
Gate 2
Mat
Time
(s)
0
Distance
Between
Gates
(m)
Horizontal
Velocity
(m/s)
Time in
flight (s)
Predicted
distance
(m)
Actual
distance
(m)
0.02
1.370802
0.27919
0.382714
0.335
0.01459
0.29378
Part 3: Taking Data (25 mins)
 Set up the target at a distance so that the ball will hit the central zone on the carbon
paper covering the target.
 Open the EasySense software package. You are interested in measuring the times
of the ball passing through the light gates and hitting the landing pad.
 From the opening menu select: timing, raw times, next, at A or B, then finish.
 Now from the Display option at top select Show Table – this will display the times
recorded.
 You can now start the experiment using start button. Release the ball and click
stop once the ball has landed.
 You are only interested in the first 3 measurements although the computer might
attempt taking 1000!
 The first and second times recorded are those of the ball triggering each light
gate respectively.
 The third time recorded is that of the ball hitting the landing pad.
 Enter these times into your Excel spreadsheet.
 Once you have transferred the data from your first run, delete this data from the
EasySense table. To do this you will need to highlight every cell by clicking on
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Physics 1 – Projectile Motion
the top cell, holding shift, and clicking the bottom cell. Now click delete on the
top toolbar to clear the cells.
Hints:
a) It might be wise to number each dot so you can measure the horizontal distance
afterwards.
b) Delete the data after each run. This will save you from having to restart the
software each time.

Perform the experiment for three or more different release points of the ball.
3.1 Produce an Excel spreadsheet showing all your results
3.2 Discuss how you expect changing the release point to affect the velocity and the
flight time.
 Perform the experiment with the changed release point and compare your
predictions with results obtained.
3.3 Comment on the comparison between your results and predictions. What effects
have you neglected in your analysis ?
Add a printout of your excel spreadsheet to your lab book.
Part 4: Launching at an angle to the horizontal (Optional)
4.1(a) Derive the expression for the flight time and the distance travelled by the ball
if it is launched at an angle  degrees to the horizontal and falls through a
distance y - express your results in terms of , y and horizontal velocity v.
(b) Explain what will happen to the horizontal distance travelled if the launch
point is raised an angle degrees to the horizontal.
(c) Discuss by considering the cases when y tends to 0 and y tends to infinity.
Further work
The following questions are related to the topic covered by this experimental tutorial.
 Exercise book questions D1 – D20, notably D11 and D13.
 Mastering Physics Dynamics 1: Motion in Two or Three Dimensions, notably the
Projectile Motion Tutorial.
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Physics 1 – Projectile Motion
Demonstrators' Answers, Hints, Marking Scheme and Equipment List
Marking Scheme
Section
1.1
1.2
1.3
2.1
2.2
3.1
3.2
3.3
Discretionary mark
TOTAL
Mark
1
1
1
1
1
1
1
1
2
10
Answers
1.1 mgh
1 2
mv
2
1.2
v  2 gh
mgh 
s  ut  12 at 2
1.3 working vertically y  12 gt 2
t  2y / g
s  ut  12 at 2
1.4 working horizontally
x  vt  2 gh  2
y
 2 yh
g
3.1 increase height – increase horizontal velocity
decrease height – decrease horizontal velocity
flight time will remain unaffected
3.2 friction from track, air resistance, precision of equipment, any other assumptions.
4.1(a) initial v HORIZONTAL  v cos 
initial vVERTICAL  v sin   gt
Vertically:
 y  v sin  .t 
1 2
gt
2
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Physics 1 – Projectile Motion
1 2
g .t  v sin  .t  y  0
2
1 
v sin   v 2 sin 2   4 g ( y )
2 
t 
1 
2 g 
2 
Flight time:
v sin   v 2 sin 2   2 gy
t 
g
We’re only interested in the positive solution, and to check the validity of the
2y
equation try for  = 0  t 
g
x  v cos  t
 v sin   v 2 sin 2   2 gy 

 v cos  


g


Horizontally: distance
2v sin  2v 2 sin  cos  v 2 sin 2


g
g
g
Consider y = 0:
 x  v cos  
Maximal when
sin2 = 1, i.e.  = 450
For y > 0 as y  
x  v cos  t
t
2y
g
 x  v cos  
2y
g
Maximal when cos  1 so   0, so the larger the value of y the smaller the
optimal launch angle for maximal distance.
flight time is changed, horizontal velocity is decreased, distance travelled will change
Equipment List:
Track with light gates fitted
Stand with boss head
Clamp
Ball
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Physics 1 – Projectile Motion
Measuring tape or meter stick
Landing Pad
Mouse mat and carbon paper
Stool
Catcher
Computer with EasySense software
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