Projectile Motion Grade 9 Science - Physics 4th Quarter

Projectile Motion Science 9 Q4

1. What is Projectile Motion?

2. Projectile A projectile is an object upon which the only force acting is gravity. Any object that is given an initial velocity and then follows a path determined entirely by gravitational acceleration.

3. Projectile Motion Projectile is a combination of uniform horizontal motion and free fall motion. Trajectory- curved path of a projectile Range (R)- horizontal displacement, dependent on the angle of projection

4. Projectile Motion Projectile motion  is a predictable path traveled by an object that is influenced only by the initial launch speed, launch angle, and the acceleration due to gravity. Two-dimensional motion of an object Vertical Horizontal

5. Projectile Motion Italian Scientist Galileo Galilei first describe projectile motion as having two components: horizontal and vertical.

6. Types of Projectile Motion Horizontal Motion of a ball rolling freely along a level surface Horizontal velocity is ALWAYS constant Vertical Motion of a freely falling object Force due to gravity Vertical component of velocity changes with time Parabolic Path traced by an object accelerating only in the vertical direction while moving at constant horizontal velocity

7. Types of Projectile Motion If air resistance is neglected, a projectile moves horizontally at a constant speed and simultaneously travels vertically with an acceleration equal to g , which is 9.8 m/s ² Note: the motion of freely falling body is a special case of projectile motion where the horizontal velocity is 0.

8. Horizontal “Velocity” Component NEVER changes, covers equal displacements in equal time periods. This means the initial horizontal velocity equals the final horizontal velocity In other words, the horizontal velocity is CONSTANT. BUT WHY?

9. Vertical “Velocity” Component Changes (due to gravity), does NOT cover equal displacements in equal time periods. Both the MAGNITUDE and DIRECTION change. As the projectile moves up the MAGNITUDE DECREASES and its direction is UPWARD. As it moves down the MAGNITUDE INCREASES and the direction is DOWNWARD.

10. Projectile Launched at an Angle If a projectile is launched at an angle either below or above the horizontal, you need to resolve the initial velocity into its horizontal and vertical components. Range- launching point which measured on the assumption that the projectile returns to the same level from which it is fired. Time symmetry- the for the projectile to reach the maximum height equals the time for it to land

11. Projectile Launched at an Angle Speed Symmetry- shows that the speed of the projectile at any height above the starting point on its way up is equal to its speed at the same height on the way down. Absolute values o the angles that these speeds make with the horizontal are also are also equal. The velocities are not equal because they point in opposite directions.

12. Examples of Projectile Motion Launching a Cannon ball

13. Kinematics of Projectile Motion 1. V O – initial velocity 2. V ox and V oy - initial horizontal and initial vertical velocities. 3. V x and V y - instantaneous horizontal and instantaneous vertical velocities 4. Ѳ – is the angle of projection.

14. X-COMPONENT Y-COMPONENT VECTORS X-DIRECTION Y-DIRECTION V d y = V oy t + gt gd

15. Impulse and Momentum Impulse produced by a force changes momentum. Linear momentum or momentum is the product of the mass of the object and its velocity. P is a symbol for momentum.

16. Impulse and Momentum It is a vector quantity and an SI unit of kg•m /s. p=mv Every moving object has momentum, which may be large or small depending on the object’s mass and velocity.

17. Sample Problem Which has a greater momentum: a cheetah with a mass of about 74kg and a running speed of up to 31m/s, or an elephant with a mass of 7000kg running at 18km/ hr ?

18. Sample Problem A delivery truck carrying 75 cavans of rice is traveling at 10.0 m/s. The mass of the truck and one cavan of rice are 3000kg and 50kg, respectively. The driver of the truck has a mass of 85kg. What is the momentum of the truck with the driver and the cavans of rice? At a certain grocery, the driver unloaded 8 cavans . What is the new momentum of the truck with the driver and the cavans of rice if the driver maintains the same speed?

19. Impulse-Momentum Theorem Impulse- the product of force and the time it acts on an object. Impulse is represented by a capital letter I. I = Ft Note: Newton’s Law of Acceleration

20. Impulse-Momentum Theorem Impulse produced by a force changes momentum. It is a vector quantity and SI unit is N*s. A force acting on an object for a time interval ∆ t changes the momentum of the object. Change in momentum of a system is equal to the impulse of the force it experience. Note: Newton’s Law of Acceleration

21. Impulse-Momentum Theorem F ∆t = mv-mv Note that ∆t= t-t Setting t = 0, you have Ft=mv-mv

22. Sample Problem A force of 56.0 N acts on 25.0 kg for 12.0 s. Find the (a) impulse produced by the force (b) resulting change in momentum of the body, and (c) speed of the body at the end of 12.0 s. Assume that the body starts from rest.

23. Sample Problem Given: m = 25kg F = 56N t = 12s v = 0

24. Solution: I = Ft = (56N)(12s) =672N.s The impulse produced by the force is equal to the change in momentum of the body. Therefore, the change in momentum is 672 kg-m/s. Using the impulse-momentum theorem, you can get Ft = mv – mv 672Ns = (25kg) * v + 0 v = 26.9m / s