Download What is a Projectile - School of Physical Education

PROJECTILE
By,
Dr. Ajay Kumar
School of Physical Education
D.A.V.V. Indore
What is a Projectile
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A projectile is an object upon which the only
force acting is gravity.
A projectile is any object which once projected
continues in motion by its own inertia and is
influenced only by the downward force of
gravity.
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A projectile may be any body/ object which is
impelled in space with some initial velocity and
the continues to move under the effect of its
own inertia. The only force now acting is
gravity.
The projectile may be an inanimate object (non
living) like as implement or may be the
performer himself or herself like in jumping
events or in gymnastics.
Examples of Projectiles
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an object dropped from rest is a projectile
(provided that the influence of air resistance is
negligible);
an object which is thrown vertically upward is
also a projectile (provided that the influence of
air resistance is negligible); and
an object is which thrown upward at an angle is
also a projectile (provided that the influence of
air resistance is negligible).
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Many students have difficulty with the concept
that the only force acting upon an upward
moving projectile is gravity.
Their conception of motion prompts them to
think that if an object is moving upward, then
there must be an upward force.
And if an object is moving upward and
rightward, there must be both an upward and
rightward force.
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Their belief is that forces cause motion; and if there is
an upward motion then there must be an upward force.
They reason, "How in the world can object be moving
moving upward if the only force acting upon it is
gravity?"
Such students do not believe in Newtonian physics (or at
least do not believe strongly in Newtonian physics).
Newton's laws suggest that forces are only required to
cause an acceleration (not a motion).
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Recall from the Newton's laws that a force is required
to keep an object in motion. This idea is simply not
true;
a force is not required to keep an object in motion. A
force is only required to maintain an acceleration.
And in the case of a projectile that is moving upward,
there is a downward force and a downward
acceleration; that is, slowing down the object which is
moving upward.
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An example of this downward force and a downward
acceleration for projectiles, can be easily understood by
a cannonball shot horizontally from a very high cliff at
a high speed. And suppose for a moment that the gravity
switch could be "turned off" such that the cannonball
would travel in the absence of gravity?
What would the motion of such a cannonball be like?
How could its motion be described? According to
Newton's first law of motion, such a cannonball would
continue in motion in a straight line at constant speed.
In the absence of all forces.
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Now suppose that the "gravity switch is turned
on" and that the cannonball is projected
horizontally from the top of the cliff. What
effect will gravity have upon the motion of the
cannonball?
Will gravity effect the cannonball's horizontal
motion? Will the cannonball travel a greater (or
shorter) horizontal distance due to the influence
of gravity?
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The answer to both of these questions is "No!“
Gravity will act downwards upon the cannonball
to effect its vertical motion.
Gravity causes a vertical acceleration, causing
the ball to drop vertically below its otherwise
straight-line, inertial path.
Gravity is the downward force upon a projectile
which influences its vertical motion and causes
the parabolic trajectory which is characteristic of
all projectiles.
Definition of Other Terms Related
with Projectile
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Parabola: Once the object is projected in space it
follows a uniform and set path during its flight
which is called the parabola.
Range: Horizontal distance covered by the object
from the point of projection to the point of fall
with the level of projection.
Time of Flight: Time of flight is the time taken by
the object from the point of projection to the
point of fall with the same level of projection.
Vertical Projection
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When a ball is allowed to fall freely its behavior
is determined by gravity.
When it is thrown straight up, its upward flight
is governed by upward acceleration due to
initial force of throw and downward force of
gravity which is slowing down the upward
acceleration of throw.
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Consequently an upward thrown ball will have
the same speed when it falls again into the hand
as it was at the time of release.
The speed (magnitude) of ball starting up will be
equal to the speed of the ball landing.
The only difference is the difference of
direction.
i.e.
–u = +v
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When any object is thrown upward, it continues
to slow down until it reaches a point at which
the upward acceleration is neutralised by the
down ward pulling force of gravity.
Horizontal Projection
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The flight path of a ball thrown horizontally is
also determined by the force of the throw and
the down ward acceleration of gravity.
A horizontally projected objects starts out
horizontally but immediately begins to follow a
downward curved path because of the additional
effect of gravity acting on it.
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Balls thrown horizontally with different forces
will have different horizontal velocities and will
travel different horizontal distance.
s = vt
But all will travel the same vertical distance
downward.
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The horizontal distance the projectile travels is
governed by both the horizontal velocity of the
object and the amount of time the object is able
to remain in the air.
Example
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A ball thrown horizontally from a height of 8
feet above the ground with a horizontal velocity
50 feet/sec, will go 35 feet before hitting the
ground.
A ball thrown with the same velocity but from a
height of four feet will go just 25 feet before
hitting the ground.
To calculate Time use the equation
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S=ut+(1/2 at2)
Where
 S= distance
 u= initial downward velocity
 a= acceleration due to gravity
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Case I
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S=ut+(1/2 at2)
4=0xt + (1/2 x 32xt²)
4=16t²
t²=4/16
t²= .25
t= .5
Case II
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S=ut+(1/2 at2)
8=0xt + (1/2 x 32xt²)
8=16t²
t²=8/16
t²=.5
t= .7
To calculate horizontal distance
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v= s/t
Where
 v= final velocity
 s = horizontal distance
 t = time
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Case - I
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v = 50 feet / sec
t = .5 sec
s = vt
s = 50 x .5
s = 25 feet
Case - II
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v = 50 feet / sec
t = .7 sec
s = vt
s = 50 x .7
s = 35 feet
Diagonal Projection
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More often than not, objects put in flight will be sent in
direction other than exactly vertical or horizontal.
They will be projected at some angle with respect to
horizontal or vertical.
If no other force acts on such object except which
propels it into space, the object’s inertia will cause it to
continue to move at the same speed at same angle.
(Newton’s Law)
But the projectile does not do this.
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It begins dropping the instant it is projected into
space.
It moves downward with an increasing velocity
according to the constant acceleration of gravity
following a flight path (the parabola).
Since this type of projectile flight has both
vertical and horizontal velocity imparted to it
initially, its flight will be determined by the
nature of both the components.
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The vertical flight of the object is the resultant of the
imparted upward vertical velocity and the downward
acceleration.
Whereas the horizontal flight is governed only by the
horizontal velocity of projection.
AS LONG AS THE OBJECT IS IN THE AIR THE
HORIZONTAL DISTANCE COVERED IS THE
PRODUCT OF THE HORIZONTAL VELOCITY
AND THE TIME OF FLIGHT.