Projectile motion of a particle

This PPT covers projectile motion of an object in a very systematic and lucid manner. I hope this PPT will be helpful for instructors as well as students.

1. PROJECTILE MOTION

2. Projectile motion Projectile motion is a motion in which an object is thrown near the earth’s surface, and it moves along the curved path under the action of gravity only.

3. Motion of a snow boarder descending from a slope

4. Motion of a rider performing a bike stunt

5. Motion of water jets coming out from nozzles

6. Assumptions used in projectile motion The effect due to air resistance is negligible. The effect due to curvature of the earth is negligible. The effect due to rotation of the earth is negligible. The acceleration due to gravity is constant over the range of motion.

7. Idealized model of projectile motion        

8. Projectile Any object which is projected in the air is called as projectile. Projectile        

9. Point of projection The point from which the object is projected in air is called as point of projection. Point of projection        

10. Velocity of projection The velocity with which an object is projected in air is called as velocity of projection. Velocity of projection        

11. Angle of projection The angle with the horizontal at which an object is projected in air is called as angle of projection. Angle of projection        

12. T rajectory The parabolic path followed by a projectile in air is called its trajectory. Trajectory        

13. Time of flight Time taken by the projectile to cover the entire trajectory is called as time of flight. Time of flight          

14. Maximum height of projectile It is the maximum vertical distance travelled by the projectile from the ground level during its motion. Maximum height        

15. Horizontal range of projectile It is the horizontal distance travelled by the projectile during entire motion. Horizontal range        

16. Is horizontal and vertical motions are interdependent? Both pink and yellow balls are falling at the same rate. Y ellow ball is moving horizontally while it is falling have no effect on its vertical motion. It means horizontal and vertical motions are independent of each other.

17. Analysis of projectile motion Motion diagram of a kicked football

18. Analysis of projectile motion       Projectile motion Vertical motion Horizontal motion       Frame - 1            

19. Analysis of projectile motion       Projectile motion Vertical motion Horizontal motion       Frame - 2            

20. Analysis of projectile motion   Projectile motion Vertical motion Horizontal motion           Frame - 3        

21. Analysis of projectile motion       Projectile motion Vertical motion Horizontal motion         Frame - 4          

22. Analysis of projectile motion       Projectile motion Vertical motion Horizontal motion       Frame - 5            

23. Analysis of projectile motion                                                      

24. Important conclusion Projectile motion is a combination of two motions: Horizontal motion with constant velocity Vertical motion with constant acceleration

25. Equation of trajectory The horizontal distance travelled by the projectile in time ‘t’ along -axis is,         The vertical distance travelled by the projectile in time ‘t’ along -axis is,         Substituting the value of ‘t’ from eq.(1) in eq.(2) we get,       This is the equation of trajectory of a projectile.   Thus is a quadratic function of . Hence the trajectory of a projectile is a parabola.   As , and are constant for a given projectile, we can write    

26. Equation for time of flight The vertical distance travelled by the projectile in time ‘t’ along -axis is,     For symmetrical parabolic path, time of ascent is equals to time of descent. For entire motion, and             This is the equation for time of flight.

27. Equation for horizontal range The equation of trajectory of projectile is given by,   This is the equation for horizontal range. For a given velocity of projection the range will be maximum when ,     For entire motion, and             Thus range of the projectile is maximum if it is projected in a direction inclined to the horizontal at an angle of .  

28. Two angles of projection for the same horizontal range The equation for horizontal range is given by,     Replacing by ,           From eq. (1) & (2) we say that ,   Thus horizontal range of projectile is same for any two complementary angles i.e. and              

29. Equation for maximum height The third kinematical equation for vertical motion is ,   At maximum height:         This is the equation for maximum height. Case-1: Angle of projection is .         Case-2: Angle of projection is .        

30. Thank you