Something on projectile motion by Sonia......

1. PROJECTILE
MOTION
Sonia

2. Content
Definition of Projectile
Definition of Projectile Motion
Types of Projectile Motion
Examples of Projectile motion
Derivation of projectile motion in 2-D
Factors Affecting Projectile Motion

3. Definition Of Projectile
A projectile is any object that once projected or dropped
continues in motion by its own inertia and is influenced only by
the downward force of gravity.
By definition, a projectile has a single force that acts upon it -
the force of gravity. If there were any other force acting upon
an object, then that object would not be a projectile. Thus, the
free-body diagram of a projectile would show a single force
acting downwards and labeled force of gravity (or simply Fgrav).
Regardless of whether a projectile is moving downwards,
upwards, upwards and rightwards, or downwards and
leftwards, the free-body diagram of the projectile is still as
depicted in the diagram at the right.
Fgrav
Free-body diagram
of a projectile

4. Definition Of Projectile
Motion
Projectile motion is a form of motion in which an object or particle (called a
projectile) is thrown near the earth's surface, and it moves along a curved path
under the action of gravity only. Example: Parabolic water trajectory

5. Types Of Projectile Motion
• Horizontal
– Motion of a ball rolling freely along a level
surface
– Horizontal velocity is ALWAYS constant
• Vertical
– Motion of a freely falling object
– Force due to gravity
– Vertical component of velocity changes with
time
• Parabolic
– Path traced by an object accelerating only in
the vertical direction while moving at
constant horizontal velocity

6. Examples Of Projectile Motion
Launching a Cannon ball

7. Examples Of Projectile Motion
Object thrown upward from a car moving in a horizontal direction

8. Derivation Of Projectile Motion in 2-D
The initial velocity
If the projectile is launched with an initial velocity , then it
can be written as
The components and can be found if the angle, is known:
If the projectile's range, launch angle, and drop height are
known, launch velocity can be found using Newton's
formula
The launch angle is usually expressed by the symbol theta,
but often the symbol alpha is used.
Initial velocity of
parabolic throwing
Components of initial
velocity of parabolic
throwing

9. Derivation Of Projectile Motion in 2-D
Kinematic quantities of projectile motion
In projectile motion, the horizontal motion and the vertical motion are
independent of each other; that is, neither motion affects the other.
Acceleration
Since there is no acceleration in the horizontal direction, the velocity in the
horizontal direction is constant, being equal to
The vertical motion of the projectile is the motion of a particle during its free
fall. Here the acceleration is constant, being equal to
The components of the acceleration are:

10. Derivation Of Projectile Motion in 2-D
Velocity
The horizontal component of the velocity of the object remains unchanged
throughout the motion. The vertical component of the velocity increases
linearly, because the acceleration due to gravity is constant. The accelerations in
the and directions can be integrated to solve for the components of velocity at
any time , as follows:
The magnitude of the velocity (under the Pythagorean theorem):

11. Derivation Of Projectile Motion in 2-D
Displacement
Displacement and coordinates of parabolic throwing
At any time , the projectile's horizontal and vertical
displacement:
The magnitude of the displacement: Displacement and
coordinates of parabolic
throwing

12. Derivation Of Projectile Motion in 2-D
Parabolic trajectory
Consider the equations,
If t is eliminated between these two equations the following equation is
obtained:
This equation is the equation of a parabola. Since ,
and are constants, the above equation is of the form
in which a and b are constants. This is the equation of a parabola, so the path
is parabolic. The axis of the parabola is vertical.

13. Derivation Of Projectile Motion in 2-D
The maximum height of projectile
The highest height which the object will reach is known
as the peak of the object's motion. The increase of the
height will last, until that is,
Time to reach the maximum height:
From the vertical displacement of the maximum height
of projectile:
Maximum height of projectile

14. Derivation Of Projectile Motion in 2-D
The maximum distance of projectile
It is important to note that the Range and the
Maximum height of the Projectile does not depend
upon mass of the trajected body. Hence Range and
Maximum height are equal for all those bodies which
are thrown by same velocity and direction. Air
resistance does not affect displacement of projectile.
The horizontal range d of the projectile is the horizontal
distance the projectile has travelled when it returns to
its initial height (y = 0).
Maximum distance of
projectile

15. Derivation Of Projectile Motion in 2-D
Time to reach ground:
From the horizontal displacement the maximum
distance of projectile:
So
Note that d has its maximum value when
which necessarily corresponds to
Maximum distance of
projectile

16. Factors Affecting Projectile
Motion
What two factors would affect projectile
motion?
– Angle
– Initial velocity
Initial Velocity
Angle

17. Thank You!