this is all about projectile motion......first few slides are only for presentation ....if needed u can ignore them.....

9. Projectile
Motion
1.

10. Projectile ??
1.

11. Important
Terms
1

12. • Projectile motion – a combination of
vertical and horizontal motions that are
completely independent of each other
• Projectile – an object or body thrown
with an initial velocity and whose
motion is influenced by the pull of
gravity
Important Terms

13. • Trajectory – the curved path of a
projectile; it is principally determined by
two types of motion: vertical and
horizontal motions
• Range (dx) – the horizontal displacement
of a projectile
Important Terms

14. • Height (dy) – the vertical displacement
of a projectile
Important Terms

15. ELEMENTS
PROJECTILE
2

16. Elements
Maximum
height
Time of
flight
Horizontal
Range

17. TYPES
PROJECTILE
3

18. Consider OX a horizontal line parallel to the
ground & OY is a vertical line perpendicular to
ground. Suppose an object is projected from
point O above the ground with velocity “u”
horizontally such that t=0 . After the project
ion the body will move under combine
effect of two perpendicular velocities.
1. Horizontal velocity “u” which remain
constant along OY throughout the
journey y.
2. Vertical velocity which increases
due to gravity.

19. Path of Projectile
Let at any time “t” the particle is located at point “p” . Here x is the distance covered
by the particle along OX & Y is the distance covered by the particle along OY.
Motion of object along OX.
Where, (because there is no acceleration along OX)
X=0+at+0
X/u=t (1)
Motion along OY:
Where, (because no initial velocity along OY)
(2)

20. Put (1) in(2)
We get,
This equation is of a parabola . Therefore the path of projectile
is parabolic in nature

21. Time of Flight

22. Horizontal Range

23. The velocity of projectile at any
instant
At any instant during the journey the
object posses 2 independent
perpendicular velocities. Vx=u
because the horizontal velocities
remains constant throughout the
journey &
Vy=uy +ayt
Vy = gt ( because uy=0)
So Resultant Velocities :
So,

24. Trajectory Of An Oblique
Projection
Consider a projectile thrown with
velocity “u” at an angle θ with the
horizontal. The velocity “u” can
be resolved into two rectangular
components i.e. ucosθ along x-axis
& usinθ along y-axis. The motion
of the projectile is two
dimensional motion. Ti can be
supposed to be made up of two
motion horizontally motion &
vertical motion.

25. Path Of Projectile
Suppose the particle at any time “t” is at point P(x,y)
X= horizontal distance
Y= vertical distance
Motion along the horizontal direction:
The position of the projectile at any time “t” along the horizontal direction is:
…………(1)

26. Motion along the vertical direction:
………….(2)
Putting (1) in(2)
This is an equation of a parabola . Hence the path of a projectile projected at some
angle with the horizontal direction from ground is a parabolic path.

27. Time Of Flight
Total time T=time of ascent(t) +time of descent(t)
=2t
T/2=t
As the particle reaches the highest point , the vertical component of
velocity of the object becomes zero.
Such that,

28. Maximum Height
Time taken to attain the maximum height is t=T/2
But ,
So,

29. Horizontal Range
We know that,