PHYSICS
Projectile Motion
•
•
MR. BALDWIN
October 24, 2013
AIM: How can we describe the path of an
object fired horizontally from a height above
the ground?
DO NOW: A ball rolls off a table top with
an initial horizontal velocity.
– Predict and draw the path that the ball will
follow.
PROJECTILE MOTION
HOW WOULD YOU DESCRIBE A PROJECTILE?
• A projectile is an object fired either above the ground horizontally or at
an angle with respect to the horizontal OR from the ground at an angle
with respect to the horizontal.
HOW WOULD YOU DESCRIBE THE PATH OF A PROJECTILE?
• The path of a projectile is always a PARABOLA.
WHAT FORCE(S) IS/ARE ACTING ON THE PROJECTILE?
• The only force (influence) acting on a projectile is GRAVITY.
THEREFORE, WHAT DO YOU THINK IS THE ACCELERATION
OF THE PROJECTILE?
• Its only acceleration is the ACCELERATION DUE TO GRAVITY, g
(9.80m/s2) always acting downwards.
CAN YOU NOW DEFINE A PROJECTILE IN
ONE CONCISE SENTENCE?
A projectile is an object
moving in two dimensions
under the influence of the
Earth's gravity alone and
following a parabolic path.
It can be understood by analyzing the horizontal and
vertical motions separately.
CHECK
Looking at the
diagram, analyze the
horizontal and vertical
velocities of the
projectile separately.
What did you observe?
• About the velocity in the x-direction?
• The velocity in the x-direction is constant (never
changes).
• What does that imply?
• The horizontal motion is uniform/constant.
• About the velocity in the y-direction?
• The velocity in the y-direction is increasing.
• What does that imply?
• The object is being accelerated downwards.
• The object is falling with a constant acceleration g.
PHYSICS
Projectiles
MR BALDWIN
25-Oct-13
AIM: How can we describe the path of an object fired
at an angle w.r.t. the horizontal?
DO NOW: A ball is projected up at an angle with
respect to the horizontal with an initial velocity.
– Predict and draw the path that the ball will
follow.
v
θ
Projectile Motion: A different view
Two balls start to fall at the same
time. The yellow ball has an initial
speed in the x-direction. The red
ball is just released (dropped).
What do you observe as
the balls fall?
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.
Projectile Motion
 In projectile motion, the
horizontal motion and the vertical
motion are independent of each
other, neither motion affects the
other.
 What is the acceleration of the
horizontal motion
 zero acceleration
What is the acceleration of the
vertical motion
 constant downward acceleration
of g
The initial velocities are
vix  vi cos
and viy  vi sin  0
RECALL FREEFALL MOTION
1
2
h  vi  t  g  t
2
1
2
h  g t  t 
2
v f  vi  g  t
v f  g t
2h
g
PHYSICS
Projectile Motion
MR. BALDWIN
30-Oct-13
AIM: How can we solve problems involving
projectiles?
DO NOW: A cannonball is shot out of a cannon at a
speed of 20 m/s at an angle of 300 to the horizontal.
Calculate the horizontal and vertical components
of its velocity?
Homework: Your homework sheet will be uploaded
onto my webpage. Get it from there. Due FRIDAY.
20 m/s
300
CHECK
vix  vi cos    20m / s  cos 30  17m / s
viy  vi sin    20m / s  sin 30  10m / s
Write out your equations of
motion for constant and
accelerated motion if you do not
have your index card handy.
How would you describe the vertical motion of a
projectile?
The vertical motion is accelerated motion. a   g
viy  vi sin  0
 There is a constant downward acceleration g in the vertical direction.
The vertical
displacement:
1 2
1 2
y  viy t  gt   vi sin   t  gt
2
2
The velocity:
v y  vi sin   gt
Projectile Motion Analyzed
How would you describe the horizontal motion of a
projectile?
 There is NO horizontal acceleration. Therefore, the motion is
uniform or constant. Horizontal velocity never changes
vix  vi cos
 The horizontal distance of a projectile is called the RANGE
R  x  vixt   vi cos  t
CHECK
• What is the acceleration of a projectile?
– Always constant g &acting downwards
• What is meant by the range of a projectile?
– Maximum horizontal distance
• What is meant by the maximum height of a projectile?
– Height at which the object stops rising
• What happens at the maximum height of a projectile? Is
the object still moving?
– Yes. Horizontally.
• What is meant by the time of flight of a projectile?
– The length of time the object is in the air
LET’S ANALYZE THE DO NOW
A cannonball is shot out of a cannon at a speed of 20
m/s at an angle of 300.
• What are the horizontal and vertical
components of its velocity?
• What maximum height did it reach?
• How long was it in the air?
• How far did it travel?
20 m/s
300
Vertically, what do we know?
a  9.80m / s 2
vi , y  10 m / s
At top of its path : v f , y  0 m / s
Therefore : v f , y  vi , y  g  t
Solving for t

Solving for ymax

t
vi , y
g
10m / s
t
 1.02 s
2
9.80m / s
1
2
 vi , y  t  g  t  5.1 m
2
Horizontally, what do we know?
vi , x  vx  17 m / s
Motion is constant
We solved for time to rise

t  1.02 s
Therefore, time of flight is twice that. t  2  1.02 s   2.04 s
CHECK. Why do you think that is so?
We solved for the time of flight
t  2.04 s
Now the Range : R  v x  t  17m / s 2.04s   34.7m
LET’S PLAY HIT THE TARGET.
http://phet.colorado.edu/sims/projectilemotion/projectile-motion_en.html
http://jersey.uoregon.edu/vl
ab/block/Block.html
19
3-6 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.
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.
Projectile Motion Is Parabolic
In order to demonstrate that
projectile motion is parabolic, we
need to write y as a function of x.
When we do, we find that it has the
form:
This is indeed
the quadratic
equation for a
parabola.