Projectile
Motion
Unit 6
Created by Kelly Rick
Projectile Motion
There are only two kinds of problems and we will
approach each separately then mix for the review:
Horizontally launched
Departure angle of 0°
Launched at an angle
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Projectile Motion and the Velocity Vector
 Any object that is
moving through the air
affected only by gravity
is called a projectile.
 The path a projectile
follows is called its
trajectory.
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Projectile Motion and the Velocity Vector
 The trajectory of a
thrown basketball
follows a special type
of arch-shaped curve
called a parabola.
 The distance a
projectile travels
horizontally is called its
range.
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Range
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Projectile Motion
It can be
understood by
analyzing the
horizontal (x) and
vertical (y)
motions
separately.
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Projectile Motion The speed in the xdirection is constant; in
the y-direction the object
moves with constant
acceleration g.
This photograph shows two
balls that start to fall at the
same time. The one on the
right has an initial speed in the
x-direction. It can be seen that
vertical positions of the two
balls are identical at identical
times, while the horizontal
position of the yellow ball
increases linearly.
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Solving Problems Involving Projectile Motion
1. Read the problem carefully, and choose the
object(s) you are going to analyze.
2. Draw a diagram.
3. Choose an origin and a coordinate system.
4. Decide on the time interval; this is the same in
both directions, and includes only the time the
object is moving with constant acceleration g.
5. Examine the x and y motions separately.
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Solving Problems Involving Projectile
Motion
6. List known and unknown quantities.
Remember that vx never changes, and that
vy = 0 at the highest point.
7. Plan how you will proceed. Use the
appropriate equations; you may have to
combine some of them.
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The famous “T” chart
quantity
distance
acceleration
Initial Velocity
Final Velocity
time
Horizontal
X motion
0 m/s2
Vertical
Y motion
-10 m/s2
0 m/s
Same
Same
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Horizontally Launched Projectiles
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Horizontal Speed
 The ball’s horizontal
velocity remains constant
while it falls because gravity
does not exert any
horizontal force.
 Since there is no force, the
horizontal acceleration is
zero (ax = 0).
 The ball will keep moving to
the right at 5 m/sec.
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Horizontal Speed & distance
 The horizontal distance a projectile moves can
be calculated according to the formula:
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Vertical Speed
 The vertical speed (vy) of the
ball will increase by 9.8
m/sec after each second.
 After one second has
passed, vy of the ball will be
9.8 m/sec.
 After the 2nd second has
passed, vy will be 19.6 m/sec
and so on.
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Solving Problems Involving
Projectile Motion
Example : Driving off a cliff.
A movie stunt driver on a
motorcycle speeds
horizontally off a 50.0-m-high
cliff. How fast must the
motorcycle leave the cliff top
to land on level ground below,
90.0 m from the base of the
cliff where the cameras are?
Ignore air resistance.
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Created by Kelly Rick
Vector Review
Vectors and Direction
Key Question:
How do we accurately
communicate length
and distance?
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Vectors and Direction
 A scalar is a quantity that
can be completely
described by one value:
the magnitude.
 You can think of
magnitude as size or
amount, including units.
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Vectors and Direction
 A vector is a quantity that
includes both magnitude
and direction.
 Vectors require more than
one number.
 The information “1
kilometer, 40 degrees east
of north” is an example of
a vector.
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Calculate a resultant vector
 An ant walks 2 meters West, 3 meters
North, and 6 meters East.
 What is the displacement of the ant?
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Finding Vector Components Graphically
 Draw a
displacement
vector as an
arrow of
appropriate length
at the specified
angle.
 Mark the angle
and use a ruler to
draw the arrow.
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Finding the Magnitude of a Vector
 When you know the x- and y- components of a vector,
and the vectors form a right triangle, you can find the
magnitude using the Pythagorean theorem.
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Created by Kelly Rick
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Projectiles Launched at an
Angle
Projectile Motion
If an object is launched at an initial angle of θ0
with the horizontal, the analysis is similar except
that the initial velocity has a vertical component.
Vx=Constant
velocity
ax=0
Horizontal: velocity is constant and acceleration is zero
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Projectile Motion
If an object is launched at an initial angle of θ0
with the horizontal, the analysis is similar except
that the initial velocity has a vertical component.
Vy=changing
velocity
ay=-10
Vyi not 0m/s
Vertical: acceleration is -10m/s/s
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Components …… and vectors
Represents the
velocity of an object
in 2D space
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Components …… and vectors
Now… we resolve the vector into its x and y
components…why? Because the combination
of the action in the x and y combined produce
the 2D motion represented below
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Components …… and vectors
Y-Component of motion
x-Component of motion
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Components of the motion
Y-Component of motion
x-Component of motion
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Practicing component form
 Draw the x and y components for the following vector…
37°
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Practicing component form
 Draw the x and y components for the following vector…
Y-component
of 18m/s
37°
x-component
of 18m/s
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Practicing component form
 Draw the x and y components for the following vector…
Y-component of 18
Sine 37=Y-COMPONENT
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Y- component= 18 (sin 37)
Y-component =10.8
SOH CAH TOA
Y-component
of 18
37°
x-component of 18m/s
COS 37=X-COMPONENT
18
X- component= 18 (cos 37)
X-component =14.4
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Practicing component form…2
 Draw the Θ and R components for the following vector…
8m
SOH CAH TOA
Θ
6m
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Practicing component form…2
 Draw the Θ and R components for the following vector…
8m
R=√x2+y2=10m
SOH CAH TOA
Θ
TanΘ=opp/adj
TanΘ = 8m/6m
Θ =Tan-1 (8/6)
Θ =53°
6m
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Note Taking Guide 1
Note Taking Guide 2
Using Math to Find Resultants
Using Math to Find Components
Vector Math Practice Sheet
Review
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3-8 Solving Problems Involving
Projectile Motion
Example 3-7: A kicked football.
A football is kicked at an angle θ0 = 37.0° with a
velocity of 20.0 m/s, as shown. Calculate (a) the
maximum height, (b) the time of travel before the
football hits the ground, (c) how far away it hits the
ground, (d) the velocity vector at the maximum height,
and (e) the acceleration vector at maximum height.
Assume the ball leaves the foot at ground level, and
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ignore air resistance and rotation
of the ball. Created by Kelly Rick
Solving Problems Involving Projectile Motion
Conceptual Example : Where does the apple land?
A child sits upright in a wagon
which is moving to the right at
constant speed as shown. The
child extends her hand and throws
an apple straight upward (from her
own point of view), while the
wagon continues to travel forward
at constant speed. If air resistance
is neglected, will the apple land (a)
behind the wagon, (b) in the
wagon, or (c) in front of the
wagon?
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Created by Kelly Rick
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Solving Problems Involving Projectile Motion
Conceptual Example : The wrong strategy.
A boy on a small hill aims his water-balloon slingshot
horizontally, straight at a second boy hanging from a
tree branch a distance d away. At the instant the water
balloon is released, the second boy lets go and falls
from the tree, hoping to avoid being hit. Show that he
made the wrong move. (He hadn’t studied physics
yet.) Ignore air resistance.
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Note Taking Guide I
Note Taking Guide II
Projectile Problems
Review
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