PROJECTILE

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PROJECTILE

• By,
• Dr. Ajay Kumar
• School of Physical Education
• D.A.V.V. Indore

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What is a Projectile

• 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.

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Examples of Projectiles

• 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.

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Definition of Other Terms Related with Projectile

• 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.

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Vertical Projection

• 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.

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Horizontal Projection

• 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.

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Example

• 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.

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To calculate Time use the equation

• Sut(1/2 at2)
• Where
• S distance
• u initial downward velocity
• a acceleration due to gravity

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Case I

• Sut(1/2 at2)
• 40xt (1/2 x 32xt²)
• 416t²
• t²4/16
• t² .25
• t .5

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Case II

• Sut(1/2 at2)
• 80xt (1/2 x 32xt²)
• 816t²
• t²8/16
• t².5
• t .7

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To calculate horizontal distance

• v s/t
• Where
• v final velocity
• s horizontal distance
• t time

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Case - I

• v 50 feet / sec
• t .5 sec
• s vt
• s 50 x .5
• s 25 feet

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Case - II

• v 50 feet / sec
• t .7 sec
• s vt
• s 50 x .7
• s 35 feet

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Diagonal Projection

• 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 objects inertia
  will cause it to continue to move at the same
  speed at same angle. (Newtons 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.