Chapter 3 Projectile motion

1. Chapter 3 Projectile motion Two Kinematics in Dimensions

2. Projectile Motion • Projectile motion is motion in two directions • Motion in the x-direction is independent of the y-direction • Motion in the y-direction is independent of the x-direction

3. Vy Vx The Full Parabola • The key to the full parabola is symmetry. • Try to identify some points of symmetry. Throw

4. Half Parabola Timing • The time of flight of a half parabolic path is equal to that of simply dropping the object from the same height. Horizontal velocity (vx) has no affect on flight time because it is not affected by gravity.

5. Jill drops the yellow ball and throws the red ball horizontally. Which ball will hit the ground first?

6. X & Y are Independent

7. Sample half parabola • A cannon nestled in the side of a cliff (d1y = 65m) fires a cannon ball at 26 . How long until the ball splashes into the sea? Fire

8. Projectile Motion Type Not all object are launch horizontally Objects can be launched at an angle

9. Recall the trajectory of the golf ball when hit with a 3 iron. • What would the trajectory of a 9 iron look like? • The loft of the club changed the launch angle.

10. Object 1 was launched at 60o • Object 2 was launched at 30o

11. Object 1 was launched from a 25m high cliff at 0o • Object 2 was launched at 60o

12. Problem Solving Strategies Solve each direction (x & y) separately Symmetry can be used when the launching & landing places are the same height. Vy 15.0m/s 12.5m/s 10.0m/s 7.50m/s 5.00m/s 2.50m/s 0.00m/s

13. A football player kicks a ball at 27m/s at an angle of 30°. Find the maximum height What is true about the vertical velocity at the maximum height? Vy Vy=0m/s 15.0m/s 12.5m/s 10.0m/s 7.50m/s 5.00m/s 2.50m/s 0.00m/s

14. v1y v1 v1x Initial Velocity Breakdown • When an object is launched at some angle, it’s initial velocity (v1) can be broken down into two components. • Horizontal Component (Vx) • Vertical Component (Vy) • What shape is formed? • Consider also the launch angle (q). Please Note: horizontal and vertical components are independent of one another. The only commonality is time. Right Triangle q

15. Important! v1 v1y v1x Initial Velocity Breakdown (Cont.) • Consider the breakdown from the previous slide again. • There are trigonometric relationships between the sides and angles of a right triangle. q

16. v1 v1y v1x Dart-X Sample Velocity Breakdown • A dart gun is fired at an angle of 30° with a muzzle velocity of 40m/s. • Calculate the components of the velocity? Horizontal Component (x) Vertical Component (y) q Make sure your calculator is in Degree mode!

17. An arrow is shot at 44m/s at an angle of 60° • Find the maximum height of the arrow. • Find the horizontal distance the arrows travels. • Find the hang time

18. Sample Partial Parabola Problem • A cannon nestled in the side of a cliff (d1y = 20m) fires a cannonball at 130m/s at a 40° angle. • What are the components of the initial velocity? Horizontal Component Vertical Component Fire

19. Sample Partial Parabola Problem • A cannon nestled in the side of a cliff (d1y = 20m) fires a cannonball at 130m/s at a 40° angle. Complete the square Fire