1. 3.3 & 3.4 Projectile Motion

2. Biblical Reference Then the archers shot arrows at your servants from the wall, and some of the king’s men died. 2 Samuel 11:24

4. Projectile - Any object which projected by some means and continues to move due to its own inertia (mass). What is projectile?

5. The yellow ball is given an initial horizontal velocity but still falls at the same rate as the red ball. The horizontal motion and the vertical motion are of the yellow ball are independent. Independent Motions

6. Horizontally Launched Projectiles Projectiles which have NO upward trajectory and NO initial VERTICAL velocity. is increasing

7. Horizontally Launched Projectiles To analyze a projectile in 2 dimensions we need 2 equations. One for the “x” direction and one for the “y” direction - Kinematic #2. Since the horizontal velocity is CONSTANT, the acceleration is ZERO! Since the projectile is launched horizontally, the INITIAL VERTICAL VELOCITY is ZERO.

8. Horizontally Launched Projectiles A plane traveling with a 100 m/s horizontal velocity is 500 m above the ground. The pilot decides to drop some “supplies” to a designated target below. (a) How long is the drop in the air? (b) How far away from point where it was launched will it land? Given: v xi = 100 m/sv yi = 0 m/sy = 500 m Find: t,  x

9. Horizontally Launched Projectiles Given: v xi = 100 m/sv yi = 0 m/sy = 500 m Find: t,  x A plane traveling with a 100 m/s horizontal velocity is 500 m above the ground. The pilot decides to drop some “supplies” to a designated target below. (a) How long is the drop in the air? (b) How far away from point where it was launched will it land?

10. Since a projectile moves in 2-dimensions, it therefore has 2 components just like a resultant vector. Projectiles move in TWO dimensions Horizontal and Vertical

11. NEVER changes, covers equal displacements in equal time periods. This means the initial horizontal velocity equals the final horizontal velocity Horizontal “Velocity” Component In other words, the horizontal velocity is constant. But Why? Gravity Does Not work horizontally to increase or decrease the velocity.

12. Changes (due to gravity), does NOT cover equal displacements in equal time periods. Vertical “Velocity” Component 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.

13. Combining the Components ComponentMagnitudeDirection HorizontalConstant VerticalChanges Together, these components produce what is called a trajectory or path. This path is parabolic in nature.

14. Vertically Launched Projectiles Since the projectile was launched at a angle, the velocity must be broken into components!!! vovo v ox v oy 

15. There are several other things to consider when solving projectile motion problems. –If it begins and ends at the same height, the “y” displacement is ZERO: y = 0 –If it begins and ends at the same height, v i = -v f Vertically Launched Projectiles

16. You will still use kinematic #2, but you must use components in the equation. vovo v ox v oy 

17. Maximum Height & Range Max Range Angle = 45  Sin(2x45) = 1 Height Angle = 90  Sin 2 (90) = 1

18. Effect of Launch Angle

19. Example A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees. (a) How long is the ball in the air? Note: The vertical displacement must equal zero for this motion. t = 0 seconds (before kicked) or t = 3.26 seconds (at the end of flight)

20. Example A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees. (b) How far away does it land? Use the Range Equation. R = 39.2 m

21. Example A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees. (b) How far away does it land? – Alternate Method Use the time from part a. It is the only variable that can be used in both the vertical and horizontal x = 39.2 m

22. Example A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees. (c) How high does the ball go in the air? Use the Height Equation. y max = 13.1 m

23. All motion is relative! All motion is measured with respect to a particular frame of reference. Frame of Reference: system for specifying the precise location of objects in space and time; background against which motion is measured. –An object’s velocity measured in one reference frame can be completely different when it is measured from another reference frame. Frames of Reference

24. Need to distinguish velocities as measured in different frames of reference. Use subscripts using two letters: –Read as: velocity of (first letter) wrt (second letter) v ac = v ab + v bc Important: v ab = -v ba Since velocity is a vector quantity, rules of vector addition and vector resolution apply Relative Velocities

25. You are walking backward in a bus at a rate of 1 m/s. Relative to the earth, the bus is moving forward at 19 m/s. –What is your velocity relative to the bus (and other passengers on the bus)? –What is your velocity relative to an observer on the side of the road? Example

26. You are driving North at 55 mph. A driver in the Southbound lane approaches you at 45 mph. –What is your velocity relative to the other driver? –What is your velocity relative to an observer on the side of the road? Example

27. Remember the Boat?... A boat moves with a velocity of 15 m/s, N in a river which flows with a velocity of 8.0 m/s W. Calculate the boat's velocity with respect to an observer on the shore. 15 m/s, N 8.0 m/s, W RvRv  The Final Answer: 17 m/s, @ 28.1  West of North

28. Albert Einstein