projectile motion
DESCRIPTION
this is all about projectile motion......first few slides are only for presentation ....if needed u can ignore them.....TRANSCRIPT
![Page 1: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/1.jpg)
WELCOME
![Page 2: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/2.jpg)
![Page 3: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/3.jpg)
![Page 4: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/4.jpg)
![Page 5: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/5.jpg)
![Page 6: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/6.jpg)
![Page 7: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/7.jpg)
![Page 8: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/8.jpg)
PHYSICS PROJECT
![Page 9: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/9.jpg)
ProjectileMotion
1.
![Page 10: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/10.jpg)
Projectile ??1.
Projectile motion is a form of motion
where a particle (called a projectile) is
thrown obliquely near the earth's surface,
it moves along a curved path. The path
followed by a projectile is called its
trajectory, which is directly influenced by
gravity (hence the curvature).
![Page 11: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/11.jpg)
ImportantTerms
1
![Page 12: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/12.jpg)
• 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
![Page 13: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/13.jpg)
• 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
![Page 14: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/14.jpg)
• Height (dy) – the vertical displacement of a projectile
Important Terms
![Page 15: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/15.jpg)
ELEMENTS
OFPROJECTILE
2
![Page 16: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/16.jpg)
Elements
Maximum height
Time of flight
Horizontal Range
![Page 17: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/17.jpg)
TYPES
OFPROJECTILEMOTION
3
![Page 18: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/18.jpg)
Projectile Given Horizontal Projection
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 projection 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.
![Page 19: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/19.jpg)
Path of ProjectileLet 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+0X/u=t (1)
Motion along OY:
Where, (because no initial velocity along OY)
(2)
,
![Page 20: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/20.jpg)
Put (1) in(2)We get,
This equation is of a parabola . Therefore the path of projectile is parabolic in nature
![Page 21: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/21.jpg)
Time of Flight
![Page 22: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/22.jpg)
Horizontal Range
![Page 23: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/23.jpg)
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 +aytVy = gt ( because uy=0) So Resultant Velocities :
So,
![Page 24: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/24.jpg)
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.
![Page 25: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/25.jpg)
Path Of ProjectileSuppose 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)
![Page 26: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/26.jpg)
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.
![Page 27: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/27.jpg)
Time Of Flight
Total time T=time of ascent(t) +time of descent(t) =2t T/2=tAs the particle reaches the highest point , the vertical component of velocity of the object becomes zero. Such that,
![Page 28: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/28.jpg)
Maximum HeightTime taken to attain the maximum height is t=T/2
But ,
So,
![Page 29: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/29.jpg)
Horizontal RangeWe know that,
![Page 30: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/30.jpg)
![Page 31: projectile motion](https://reader033.vdocuments.mx/reader033/viewer/2022061117/54664b44af79595c6f8b48df/html5/thumbnails/31.jpg)
EFFORTS BY:-KARNIK SINGHXI-A 11