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Projectile MotionProjectile Motion
The Path of a ProjectileThe Path of a Projectile
An object thrown off a cliffA basketball free throwA golf shotA cannon ball
Trajectory
The path (trajectory)of a projectile is a parabola
Parabolic motion of a projectile
Horizontal and vertical motion are independent (90°)
There are the two components of the projectile's velocity – horizontal vX and vertical vY .
The horizontal component of it’s velocity does not change.
vX is constant
Gravity is the only force
Horizontal and vertical motion are independent!
Describe the Trajectory…Describe the Trajectory…
The projectile will move along it’s path in both the horizontal (x) direction and the vertical (y) direction at the same time.
The two directions are independent of each other.
Example
1. A rock is thrown horizontally from a high cliff at 40 m/s.
What is the horizontal component of its velocity 3 seconds later?
. A rock is thrown horizontally from a high cliff at 40 m/s.
What is the vertical component of its velocity 3 seconds later?
. A rock is thrown horizontally from a high cliff at 40 m/s.
What is the magnitude of the velocity vector 3 seconds later?
. A rock is thrown horizontally from a high cliff at 40 m/s.
What is the direction of the velocity vector 3 seconds later?
homework
Review Book: Read pg 39-41 Text Book: Read pg 146 - 150 Do problems 1-3 on page 150 in text
Do Now
An object is thrown outward from a cliff with a horizontal velocity of 20m/s. Object takes 15 s to reach the bottom of the cliff (ignore air resistance). Calculate:
1.The height of the cliff
2.The horizontal distance traveled by the object by the time it reaches the ground
Determining the HeightDetermining the Height
You can determine the height at any point in the trajectory!
2
2
1attvy y
What is acceleration?What is acceleration?
In the y direction a is always the acceleration of gravity, g.
Therefore,
2
2
1gttvy y
Horizontal velocity is 20m/s. Object takes 15 s to reach the
bottom of the cliff 1. The height of the cliff
) m 1100 (i.e., 5.1102
)15)(/8.9(2
10
2
1
22
2
downwardmy
ssmy
gttvy y
Determining the RangeDetermining the Range
You can determine the displacement (range) of a projectile any any point
along the trajectory.
tvx x
Horizontal velocity is 20m/s. Object takes 15 s to reach the
bottom of the cliff 2. The horizontal distance traveled by the
object by the time it reaches the ground
mssmx
tvx x
300)15)(/.20(
Consider an object such as a cannonball that is fired at an
angle to the ground If the initial velocity of
the object is vi and the angle is θ, we must resolve the x- and y- components.
v
sin
cos
iiy
ii
vv
vv x
vX is constant vy changes
Some Other Important NotesSome Other Important Notes
At the highest point of the trajectory, it is the exact midpoint of the time.
It takes the projectile half of the time to get to the top.
Still More NotesStill More Notes
When the projectile gets to the top, it has to stop going up and start going down.
Therefore, the velocity in the y-direction at the highest point is zero for a split second.
and Still More Notesand Still More Notes
As the projectile starts to fall down, it is simply in free fall.
The velocity in the x-direction remains constant throughout the entire trajectory.
Trajectory and Range Maximum range
is at 45° Low and high
trajectory cover the same distance.
30 and 60 10 and 80 25 and…
Component of Motion
Equation
X Acceleration
Y Acceleration
X Velocity
Y Velocity
X Position
Y Position
Homework
Test Corrections Review book pg 41-42 # 74 -86 Show all
work
Example: A ball is thrown with an initial velocity of 25 m/s at 40º to the horizontal.
1. What is vx at the highest point?
19 m/s
2. What is vy at the highest point?
0 m/s
smv
smv
iy
ix
/1640sin25
/1940cos25
A ball is thrown with an initial velocity of
25 m/s at 40º to the horizontal.3. What is the speed at the highest point?
19 m/s
4. How long does it take the ball to get to its highest point?
st
t
gtvv yy if
6.18.9/16
)8.9(160
Example 2
Courtney kicks a soccer ball @ rest on level ground giving it an initial velocity of 7.8 m/s @ an angle of 32 degrees.
a)How long will the ball be in the air?
b)How high will the ball go?
c)What will be its range?
Let’s Try another Problem!Let’s Try another Problem!
A stone is thrown horizontally at a speed of 5.0 m/s from the top of a cliff 78.4 m high
1. How long does it take the stone to reach the bottom of the cliff?
Problem continued…Problem continued…
2. How far from the base of the cliff does the stone strike the ground?
3. What are the horizontal and vertical components of the velocity of the stone just before it hits the ground?
and Another Problem…and Another Problem…
A steel ball rolls with a constant velocity on a tabletop 0.950 m high. It rolls off and hits the ground 0.352 m from the edge of the table. How fast was the ball rolling?