Teaching Topics:
Projectiles in M1
Stephen Lee
Abstract
• Techniques and strategies for teaching
Projectiles in M1 will be given in this
session, along with useful examples to
enable students to grasp the key
concepts.
Introduction
Starter exercise
• Projectiles is a topic that builds upon the
basics of motion in one dimension
What projectiles occur in ‘real’ life?
• It is an application which many students
find interesting, yet one with which they
can get lost in the detail
• Javelin, Darts, Archery, Football, Tennis,
Golf and many, many more sports!
• Non-sport examples:
– Gun shot, canons, fireworks
• Clear presentation and statements are key
Assumptions
Students need to know the assumptions that
are made about the motion, namely:
MEI M1 Specification
PROJECTILES
The motion
of a projectile
M1y Be able to formulate the equations of motion of a
1 projectile.
2 Know how to find the position and velocity at any time of
a projectile, including the maximum height and range.
• A projectile is a particle
• It is not powered
• The air has no effect on motion
3 Be able to find the initial velocity of a projectile given
sufficient information.
4 Be able to eliminate time from the component equations
that give the horizontal and vertical displacement in terms
of time.
5 Be able to solve problems involving projectiles.
• Drop two balls example!
1
Nice 1-dimension question
Question solution
(Past exam question)
(i) At the maximum height v=0
(ii) Find displacement for particle 1 after time t
Find displacement for particle 2 after time t
Then EITHER:
Equate displacements and solve for t
OR
Sub in the given value for t to show the
displacement is the same
Starter for 2-D
Starter for 2-D
• Throw a (soft? juggling?) ball between students
Points to try and draw out from the exercise
Ask questions:
• What shape is the trajectory?
• How can you vary this?
• How/why does the ball ‘get going’?
• What happens to it once it leaves your hand?
• What forces act upon it once in flight?
• Shape is parabolic, but is dependent upon the
initial speed and angle of the throw
• You have to give the ball the initial ‘impetus’ but
then it acts ‘freely’
• Once ‘in motion’ need to get students to see that
there is no other force than gravity acting
2-D Projectiles
2-D Projectiles
• The velocity of a projectile is split into two
components, horizontal and vertical. This is the
standard way to solve projectiles questions.
• The equations of motion are then applied to
each component of velocity. The main ones
used are:-
2
Time of flight:
Range and Max height:
Projectiles
Solution strategy
Solution strategy
Part (iv) direction of motion
3
Why is the path of a projectile parabolic?
Solution strategy
y
20ms-1
Assume
g = 10 ms-2
60o
x
Displacement and velocity
components:
initial velocity
Horizontal +
component
20cos60o
acceleration
velocity at time, t
(v=u+at)
displacement at time,
t (s=ut+at2/2)
0
20cos60o
Vertical
component
+
20sin60o
-10
20sin60o-
x = 20t cos 60
10t
t=
20tcos60o
20tsin60o- 5t2
x
20 cos 60
y = 20t sin 60 − 5t 2
x
x
⎛
⎞
⎛
⎞
y = 20 ⎜
⎟ sin 60 − 5 ⎜
⎟
⎝ 20 cos 60 ⎠
⎝ 20 cos 60 ⎠
x
⎛
⎞
y = x tan 60 − 5 ⎜
⎟
⎝ 20 cos 60 ⎠
2
2
Simulations Overview
Key
• Autograph examples
• The force that initiates motion is a contact force.
Once the motion of the ball is initiated, the role
of contact force is over. It does not subsequently
affect or change the velocity of the ball as the
contact is lost.
• Geogebra train example
• Geogebra past paper
(see ICT session 6b)
• Geogebra golf cliff shot investigation
(See Stretching B2)
• Remember that RESULTANT FORCE is
therefore only the particle’s weight (mass x
gravity) NOT what is actually its velocity!
• Draw a diagram if you are considering what the
velocity is at a given time
4
Key
• Need to make the distinction with the
object’s velocity at a given time, i.e. horiz
constant, vertical changing, hence
resultant changes.
• Check whether a projectile starts and
lands at the same vertical height!
5