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

2. What is a Projectile A projectile is an object upon which the only force acting is gravity. 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. 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.inertia

3. 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. 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. 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.

4. Examples of Projectiles an object dropped from rest is a projectile (provided that the influence of air resistance is negligible); 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 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). an object is which thrown upward at an angle is also a projectile (provided that the influence of air resistance is negligible).

6. Many students have difficulty with the concept that the only force acting upon an upward moving projectile is gravity. 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. 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. And if an object is moving upward and rightward, there must be both an upward and rightward force.

7. Their belief is that forces cause motion; and if there is an upward motion then there must be an upward force. 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?" 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). 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).

8. Recall from the Newton's laws that a force is required to keep an object in motion. This idea is simply not true; 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. 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. 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.

9. 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? 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. 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. Newton's first law of motion Newton's first law of motion

11. 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? 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? Will gravity effect the cannonball's horizontal motion? Will the cannonball travel a greater (or shorter) horizontal distance due to the influence of gravity?

13. The answer to both of these questions is "No!“ The answer to both of these questions is "No!“ Gravity will act downwards upon the cannonball to effect its vertical motion. 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 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. Gravity is the downward force upon a projectile which influences its vertical motion and causes the parabolic trajectory which is characteristic of all projectiles.

14. 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. 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. 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. 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.

15. Vertical Projection When a ball is allowed to fall freely its behavior is determined by gravity. 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. 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.

16. 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. 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 speed (magnitude) of ball starting up will be equal to the speed of the ball landing. The only difference is the difference of direction. The only difference is the difference of direction. i.e. – u = + v i.e. – u = + v

17. 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. 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.

18. 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. 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. 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.

19. Balls thrown horizontally with different forces will have different horizontal velocities and will travel different horizontal distance. 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. But all will travel the same vertical distance downward.

20. 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. 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.

21. 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 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. A ball thrown with the same velocity but from a height of four feet will go just 25 feet before hitting the ground.

22. To calculate Time use the equation S=ut+(1/2 at 2) S=ut+(1/2 at 2) Where Where S= distance S= distance u= initial downward velocity u= initial downward velocity a= acceleration due to gravity a= acceleration due to gravity

23. Case I S=ut+(1/2 at 2) S=ut+(1/2 at 2) 4=0xt + (1/2 x 32xt²) 4=0xt + (1/2 x 32xt²) 4=16t² 4=16t² t²=4/16 t²=4/16 t²=.25 t²=.25 t=.5 t=.5

24. Case II S=ut+(1/2 at 2) S=ut+(1/2 at 2) 8=0xt + (1/2 x 32xt²) 8=0xt + (1/2 x 32xt²) 8=16t² 8=16t² t²=8/16 t²=8/16 t²=.5 t²=.5 t=.7 t=.7

25. To calculate horizontal distance v= s/t v= s/t Where Where v= final velocity v= final velocity s = horizontal distance s = horizontal distance t = time t = time

26. Case - I v = 50 feet / sec v = 50 feet / sec t =.5 sec t =.5 sec s = vt s = vt s = 50 x.5 s = 50 x.5 s = 25 feet s = 25 feet

27. Case - II v = 50 feet / sec v = 50 feet / sec t =.7 sec t =.7 sec s = vt s = vt s = 50 x.7 s = 50 x.7 s = 35 feet s = 35 feet

28. Diagonal Projection More often than not, objects put in flight will be sent in direction other than exactly vertical or horizontal. 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. 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) 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. But the projectile does not do this.

29. It begins dropping the instant it is projected into space. 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). 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. 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.

30. The vertical flight of the object is the resultant of the imparted upward vertical velocity and the downward acceleration. 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. 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. 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.