PROJECTILEPROJECTILE

By,By,Dr. Ajay KumarDr. Ajay Kumar

School of Physical EducationSchool of Physical EducationD.A.V.V. IndoreD.A.V.V. Indore

What is a ProjectileWhat is a Projectile

A projectile is an object upon which A projectile is an object upon which the only force acting is gravity. the only force acting is gravity.

A projectile is any object which once A projectile is any object which once projectedprojected continues in motion by its continues in motion by its own own inertia and is influenced only by and is influenced only by the downward force of gravity. the downward force of gravity.

A projectile may be any body/ object A projectile may be any body/ object which is impelled in space with some which is impelled in space with some initial velocity and the continues to initial velocity and the continues to move under the effect of its own inertia. move under the effect of its own inertia. The only force now acting is gravity.The only force now acting is gravity.

The projectile may be an inanimate The projectile may be an inanimate object (non living) like as implement or object (non living) like as implement or may be the performer himself or herself may be the performer himself or herself like in jumping events or in gymnastics.like in jumping events or in gymnastics.

Examples of ProjectilesExamples of Projectiles

an object dropped from rest is a projectile an object dropped from rest is a projectile (provided that the influence of air (provided that the influence of air resistance is negligible); resistance is negligible);

an object which is thrown vertically an object which is thrown vertically upward is also a projectile (provided that upward is also a projectile (provided that the influence of air resistance is the influence of air resistance is negligible); and negligible); and

an object is which thrown upward at an an object is which thrown upward at an angle is also a projectile (provided that the angle is also a projectile (provided that the influence of air resistance is negligible). influence of air resistance is negligible).

Many students have difficulty with the Many students have difficulty with the concept that the only force acting upon concept that the only force acting upon an upward moving projectile is gravity. an upward moving projectile is gravity.

Their conception of motion prompts Their conception of motion prompts them to think that if an object is them to think that if an object is moving upward, then there moving upward, then there mustmust be an be an upward force. upward force.

And if an object is moving upward and And if an object is moving upward and rightward, there rightward, there mustmust be both an be both an upward and rightward force. upward and rightward force.

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

They reason, "How in the world can object be They reason, "How in the world can object be moving moving upward if the only force acting moving moving upward if the only force acting upon it is gravity?" upon it is gravity?"

Such students do not Such students do not believebelieve in Newtonian in Newtonian physics (or at least do not believe strongly in physics (or at least do not believe strongly in Newtonian physics). Newton's laws suggest Newtonian physics). Newton's laws suggest that forces are only required to cause an that forces are only required to cause an acceleration (not a motion). acceleration (not a motion).

Recall from the Newton's laws that a force is Recall from the Newton's laws that a force is required to keep an object in motion. This required to keep an object in motion. This idea is simply idea is simply notnot true; true;

a force is a force is notnot required to keep an object in required to keep an object in motion. A force is only required to maintain motion. A force is only required to maintain an acceleration. an acceleration.

And in the case of a projectile that is moving And in the case of a projectile that is moving upward, there is a downward force and a upward, there is a downward force and a downward acceleration; that is, slowing downward acceleration; that is, slowing down the object which is moving upward.down the object which is moving upward.

An example of this downward force and a An example of this downward force and a downward acceleration for projectiles, can be downward acceleration for projectiles, can be easily understood by a cannonball shot easily understood by a cannonball shot horizontally from a very high cliff at a high speed. horizontally from a very high cliff at a high speed. And suppose for a moment that the And suppose for a moment that the gravity switchgravity switch could be "turned off" such that the cannonball could be "turned off" such that the cannonball would travel in the absence of gravity? would travel in the absence of gravity?

What would the motion of such a cannonball be What would the motion of such a cannonball be like? How could its motion be described? like? How could its motion be described? According to According to Newton's first law of motion, such a , such a cannonball would continue in motion in a straight cannonball would continue in motion in a straight line at constant speed. In the absence of all line at constant speed. In the absence of all forces.forces.

Now suppose that the "gravity switch is Now suppose that the "gravity switch is turned on" and that the cannonball is turned on" and that the cannonball is projected horizontally from the top of projected horizontally from the top of the cliff. What effect will gravity have the cliff. What effect will gravity have upon the motion of the cannonball? upon the motion of the cannonball?

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

The answer to both of these questions is The answer to both of these questions is "No!“"No!“

Gravity will act downwards upon the Gravity will act downwards upon the cannonball to effect its vertical motion. cannonball to effect its vertical motion.

Gravity causes a vertical acceleration, Gravity causes a vertical acceleration, causing the ball to drop vertically below its causing the ball to drop vertically below its otherwise straight-line, inertial path. otherwise straight-line, inertial path.

Gravity is the downward force upon a Gravity is the downward force upon a projectile which influences its vertical projectile which influences its vertical motion and causes the parabolic trajectory motion and causes the parabolic trajectory which is characteristic of all projectiles. which is characteristic of all projectiles.

Definition of Other Terms Definition of Other Terms Related with ProjectileRelated with Projectile

Parabola: Once the object is projected in Parabola: Once the object is projected in space it follows a uniform and set path space it follows a uniform and set path during its flight which is called the during its flight which is called the parabola.parabola.

Range: Horizontal distance covered by the Range: Horizontal distance covered by the object from the point of projection to the object from the point of projection to the point of fall with the level of projection.point of fall with the level of projection.

Time of Flight: Time of flight is the time Time of Flight: Time of flight is the time taken by the object from the point of taken by the object from the point of projection to the point of fall with the projection to the point of fall with the same level of projection.same level of projection.

Vertical ProjectionVertical Projection

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

When it is thrown straight up, its When it is thrown straight up, its upward flight is governed by upward flight is governed by upward acceleration due to initial upward acceleration due to initial force of throw and downward force force of throw and downward force of gravity which is slowing down of gravity which is slowing down the upward acceleration of throw.the upward acceleration of throw.

Consequently an upward thrown ball Consequently an upward thrown ball will have the same speed when it falls will have the same speed when it falls again into the hand as it was at the again into the hand as it was at the time of release.time of release.

The speed (magnitude) of ball starting The speed (magnitude) of ball starting up will be equal to the speed of the up will be equal to the speed of the ball landing.ball landing.

The only difference is the difference The only difference is the difference of direction.of direction.

i.e. – u = + vi.e. – u = + v

When any object is thrown upward, When any object is thrown upward, it continues to slow down until it it continues to slow down until it reaches a point at which the upward reaches a point at which the upward acceleration is neutralised by the acceleration is neutralised by the down ward pulling force of gravity.down ward pulling force of gravity.

Horizontal ProjectionHorizontal Projection

The flight path of a ball thrown The flight path of a ball thrown horizontally is also determined by the horizontally is also determined by the force of the throw and the down ward force of the throw and the down ward acceleration of gravity.acceleration of gravity.

A horizontally projected objects starts A horizontally projected objects starts out horizontally but immediately out horizontally but immediately begins to follow a downward curved begins to follow a downward curved path because of the additional effect path because of the additional effect of gravity acting on it.of gravity acting on it.

Balls thrown horizontally with Balls thrown horizontally with different forces will have different different forces will have different horizontal velocities and will travel horizontal velocities and will travel different horizontal distance.different horizontal distance.

s = vts = vt But all will travel the same vertical But all will travel the same vertical

distance downward.distance downward.

The horizontal distance the The horizontal distance the projectile travels is governed by projectile travels is governed by both the horizontal velocity of the both the horizontal velocity of the object and the amount of time the object and the amount of time the object is able to remain in the air.object is able to remain in the air.

ExampleExample

A ball thrown horizontally from a A ball thrown horizontally from a height of 8 feet above the ground height of 8 feet above the ground with a horizontal velocity 50 with a horizontal velocity 50 feet/sec, will go 35 feet before feet/sec, will go 35 feet before hitting the ground.hitting the ground.

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

To calculate Time use the To calculate Time use the equationequation

S=ut+(1/2 atS=ut+(1/2 at2)2)

WhereWhere S= distance S= distance u= initial downward velocityu= initial downward velocity a= acceleration due to gravitya= acceleration due to gravity

Case ICase I

S=ut+(1/2 atS=ut+(1/2 at2)2)

4=0xt + (1/2 x 32xt²)4=0xt + (1/2 x 32xt²) 4=16t²4=16t² t²=4/16t²=4/16 t²= .25t²= .25 t= .5t= .5

Case IICase II

S=ut+(1/2 atS=ut+(1/2 at2)2)

8=0xt + (1/2 x 32xt²)8=0xt + (1/2 x 32xt²) 8=16t²8=16t² t²=8/16t²=8/16 t²=.5t²=.5 t= .7t= .7

To calculate horizontal To calculate horizontal distance distance

v= s/tv= s/t Where Where v= final velocityv= final velocity s = horizontal distances = horizontal distance t = timet = time

Case - ICase - I

v = 50 feet / secv = 50 feet / sec t = .5 sect = .5 sec s = vts = vt s = 50 x .5s = 50 x .5 s = 25 feets = 25 feet

Case - IICase - II

v = 50 feet / secv = 50 feet / sec t = .7 sect = .7 sec s = vts = vt s = 50 x .7s = 50 x .7 s = 35 feets = 35 feet

Diagonal ProjectionDiagonal Projection

More often than not, objects put in flight More often than not, objects put in flight will be sent in direction other than exactly will be sent in direction other than exactly vertical or horizontal. vertical or horizontal.

They will be projected at some angle with They will be projected at some angle with respect to horizontal or vertical.respect to horizontal or vertical.

If no other force acts on such object except If no other force acts on such object except which propels it into space, the object’s which propels it into space, the object’s inertia will cause it to continue to move at inertia will cause it to continue to move at the same speed at same angle. (Newton’s the same speed at same angle. (Newton’s Law)Law)

But the projectile does not do this.But the projectile does not do this.

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

It moves downward with an increasing It moves downward with an increasing velocity according to the constant velocity according to the constant acceleration of gravity following a flight acceleration of gravity following a flight path (the parabola).path (the parabola).

Since this type of projectile flight has Since this type of projectile flight has both vertical and horizontal velocity both vertical and horizontal velocity imparted to it initially, its flight will be imparted to it initially, its flight will be determined by the nature of both the determined by the nature of both the components.components.

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

Whereas the horizontal flight is governed Whereas the horizontal flight is governed only by the horizontal velocity of only by the horizontal velocity of projection.projection.

AS LONG AS THE OBJECT IS IN THE AIR AS LONG AS THE OBJECT IS IN THE AIR THE HORIZONTAL DISTANCE COVERED THE HORIZONTAL DISTANCE COVERED IS THE PRODUCT OF THE HORIZONTAL IS THE PRODUCT OF THE HORIZONTAL VELOCITY AND THE TIME OF FLIGHT.VELOCITY AND THE TIME OF FLIGHT.