The presentation has educators as its audience. It describes ways of teaching the chapter for learners' understanding. Note that the presentation emphasizes methods of telling stories when interpreting graphs.

1. Physical Sciences workshop 23 February 2017
Projectile motion (graphs and calculations)
Presenter: Linford Molaodi
Masemola High School
Apel Cluster
Linford Molaodi Masemola High School Email:linford.mldi@gmail.com

2. Concepts
Free-fall
-Description of motion in which the only force acting on the body is
gravitational force
Projectile motion
• Can either be free-fall or non-free fall
• Free-fall is a special case of projectile motion
• Projectile-an object projected (thrown or dropped with respect to the
horizontal, at times at an angle with the horizontal)
N.B. Definitions are many, but the fact remains, projectile may be either
free-fall or non.

3. Can a tennis, at any instance be regarded as
projectile?

4. Introduction

5. Valentines Tips
Love is
in the Air
Is a falling couple falling freely?

6. Work problem: 2012 Feb-March, National

7. Before working on any problem with graph
provided:
• Visualize the projectile’s path
• Interpret your graphs in words before even reading the statement
provided
• Tell the Story...Live it and Own it. We all remember our cultural story
tails.
• Compare your predicted interpretation with the information given
• Scrutinize the information or abstract for at least 3 times
• Write or highlight important information given

8. With graph not provided
• Highlight information you may think it is going to be of great
assistance when you have to draw your graphs
• Pay close attention to the questions and the diction utilized

9. Projectile motion tricks: diction
• Recognize the difference between the words “dropped” and
“thrown”
• When dropped, you can assume the initial velocity=0
• When thrown (either up or down), a force is being applied to give
the projectile an initial velocity. Hence vi ≠ 0
Differentiate between:
• Position-time graph
• Velocity-time graph
• and acceleration-time graphs

10. Spot the difference between the graphs
Velocity vs time Position vs time
Acceleration vs time
.
Time (s)
Acceleration(m.s-2)
+
_

11. Tell the story (Interpretation)
• Taking downward as positive
• The black horizontal line is constant
• Signifying the acceleration does not change throughout
• This is gravitational acceleration, with a magnitude of 9.8 m.s-2
• Due to our choice of direction, our gravitational acceleration is be
assigned positive (hence, drawn in the positive quadrant of the graph)
• If our downward motion were to be taken as negative, the black
horizontal line would be drawn up in the negative quadrant (the fourth
one)
• THE AREA OF THIS GRAPH RESULTS IN VELOCITY OF THE PROJECTILE

12. Velocity-time graph’s face
x y z k

13. Live the Story
• Assume the upward motion is taken as positive
• The projectile is dropped from a certain height. How do we know
this?
• When a projectile is dropped (oriented downwards) its velocity
increases
• By sheer scrutiny on the graph, the velocity increases in the
negative direction.
• The projectile thus bounces off at point x (note the vertical
dotted line)
• The graph commences in the positive direction, meaning the
object has changed directions (we are thus convinced it has
bounced…for the first time)

14. Own the Story
• The projectile goes up. How do we know this?
• Answer: the velocity decreases, and at maximum height, it reaches 0
• It thus came down (not bounced off this time)…increasing its velocity. Its
direction changed at point y
• Furthermore, the projectile bounced off for the second time at point z,
changing directions.
• It again, has its velocity decreasing in the positive direction and reached
the maximum height (a point where its v=0…indicate at point k)
• And finally, the object changed directions, going down (indicated by the
line below the 0-axis line).

15. Tricky tricky….
 How many times has the projectile bounced off?
 Answer: we have two dotted vertical lines, marked x and z.
Thus, it has bounced twice.
How do you make calculations without using equations of
motion?
 The gradient of v vs time graph indicates the acceleration of
the projectile
 The area under this graph is the displacement of the
projectile

16. Position-time graph’s face

17. Position-time graph’s face
• This indicates the path undertaken by the projectile
• According to the graph, the object was dropped from a height of 1.8 m,
reaching the ground at t1
• The object bounces off at time, t2 .
• Note that there is a slight difference (region) between t1 and t2.
• This region symbolizes, the projectile has spent a little time in contact
with the ground (very important). In drawing up a velocity-time graph,
you would indicated this phenomena by having two separately dotted
vertical lines
• The same phenomena is observed furthermore between t3 and t4.

18. Tricky tricky…
• How many times has the projectile bounced
• Answer. Lay your focus on the horizontal axis upon which the
projectile bounces. You will notice that the projectile was in
contact with floor, twice.

19. Interpreting the graph (Activity) Tell the Story
What do you spot? Tell the story
• An object thrown up at a velocity of 25.5 m.s
• An upward motion is taken as negative. How do we know this?
• The object commences at 25.5 velocity.
• The velocity decreases and reaches 0 axis line
• When an object is thrown up, its velocity decreases gradually due
to effect of gravitational force
• As the projectile reaches its maximum height from its point of
departure, its velocity is zero (0)
• We now have enough evidence to say it was moving up. If the
projectile were projected down, its velocity would increase.
N.B we are still on the first triangle in the negative direction

20. Interpretation cont… Live the Story
Immediately you notice the motion line jumping the x-axis line, know
that the object changes direction.
• You have notice that in the previous slide we dealt with the negative
quadrant. The projectile reached the 0 axis line and exceeded into the
first quadrant (the positive side)
• At 2.6 seconds, the object reached the maximum height and changed
direction (into the positive direction)
• This implies it comes down (in the positive direction)
• Its velocity increases gradually until it reaches its initial point of
departure (assuming it’s the ground) at velocity of 15 m.s-1.
• The vertical line at x (seconds) portrays a bounce
• Interpreting the graph (Activity)

21. Interpretation cont…Own the Story
• At time x, the projectile bounced at the velocity of 11.8 m.s-1.
• It went up, in the negative direction, with a decrease in velocity
until it reaches its maximum height (v=0)
• It thus, returned in the positive direction at lesser velocity
• The entire motion took 6.3 seconds
Interpreting the graph (Activity)

22. N.B
Interpret graphs carefully before reading the scenario provided or
working on any calculations

23. Calculations and exam tricks
• Decide on a reference point
• How to select and utilize a formula
• No marks for formula without substitution

24. Did you take note resources used
throughout?
 Coloured chalks (R5)
 Tennis (Borrow from learners)
 Laptop (I have proof most schools do have them)
 Powerpoint (Very easy to use)
 PhET Simulation (Free software)
 And Myself