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# projectile motion

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

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• Presentations are a powerful communication medium.
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• ### projectile motion

1. 1. Projectile Motion 1.
2. 2. Projectile ?? 1.
3. 3. Important Terms 1
4. 4. • 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
5. 5. • 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
6. 6. • Height (dy) – the vertical displacement of a projectile Important Terms
7. 7. ELEMENTS PROJECTILE 2
8. 8. Elements Maximum height Time of flight Horizontal Range
9. 9. TYPES PROJECTILE 3
10. 10. 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.
11. 11. 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)
12. 12. Put (1) in(2) We get, This equation is of a parabola . Therefore the path of projectile is parabolic in nature
13. 13. Time of Flight
14. 14. Horizontal Range
15. 15. 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,
16. 16. 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.
17. 17. 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)
18. 18. 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.
19. 19. 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,
20. 20. Maximum Height Time taken to attain the maximum height is t=T/2 But , So,
21. 21. Horizontal Range We know that,
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