1. Two-Dimensional Motion

2. One-Dimensional Motion An object moving only in one direction, either in x-direction OR y- direction. An object moving only in one direction, either in x-direction OR y- direction. Examples x-direction Examples x-direction Car, walking, running... Car, walking, running... Examples y-direction Examples y-direction Freefall Freefall

3. Two-Dimensional Motion Motion of an object traveling in 2 directions. It can be described by separating the motion into horizontal (x) components and vertical (y) components of: Motion of an object traveling in 2 directions. It can be described by separating the motion into horizontal (x) components and vertical (y) components of: displacement, velocity and acceleration. displacement, velocity and acceleration.

4. Projectiles Fired Horizontally ViVi y x Displacement - Displacement in the X direction - Displacement in the Y direction

5. Projectiles Fired Horizontally ViVi V iy V ix Velocity - Velocity in the X direction - Velocity in the Y direction

6. Projectiles Fired Horizontally Although both horizontal and vertical motion occur simultaneously, they will act INDEPENDENTLY of each other. (ignoring air friction) Although both horizontal and vertical motion occur simultaneously, they will act INDEPENDENTLY of each other. (ignoring air friction)

7. Projectiles Fired Horizontally Although both horizontal and vertical motion occur simultaneously, they will act INDEPENDENTLY of each other. (ignoring air friction) Although both horizontal and vertical motion occur simultaneously, they will act INDEPENDENTLY of each other. (ignoring air friction)

8. Projectiles Fired Horizontally Although both horizontal and vertical motion occur simultaneously, they will act INDEPENDENTLY of each other. (ignoring air friction) Although both horizontal and vertical motion occur simultaneously, they will act INDEPENDENTLY of each other. (ignoring air friction)

9. Projectiles Fired Horizontally Vertical motion will be identical to that of a free-falling object. Vertical motion will be identical to that of a free-falling object. As time increases, the vertical velocity will increase, then decrease because of GRAVITY As time increases, the vertical velocity will increase, then decrease because of GRAVITY a y = g = 9.8 m/s 2 Horizontal velocity will remain CONSTANT (ignoring air resistance) Horizontal velocity will remain CONSTANT (ignoring air resistance) a x = 0 m/s 2

10. Projectiles Fired Horizontally ViVi a y = g a x = 0 Acceleration - Acceleration in the y- direction is gravity - Acceleration in the x- direction is ZERO

11. Projectiles Fired Horizontally Finding Distance Traveled Vertically (y) Finding Distance Traveled Vertically (y) dy = v iy t + 1/2at 2 Finding Distance Traveled Horizontally (x) Finding Distance Traveled Horizontally (x) dx = v ix t + 1/2at 2

12. Projectiles Fired Horizontally Finding Time and Vertical Velocity Finding Time and Vertical Velocity ONLY depends on vertical (y) component ONLY depends on vertical (y) component Treat the problem like a free-fall Treat the problem like a free-fall Example... Example...

13. Projectiles Fired At An Angle Two-Dimensional Motion

14. Projectiles At An Angle Vertical motion (y) will act independently of horizontal motion (x) Vertical motion (y) will act independently of horizontal motion (x)

15. Projectiles At An Angle The initial velocity (v i ) can be separated into its horizontal and vertical components using trig. The initial velocity (v i ) can be separated into its horizontal and vertical components using trig.

16. Vertical Motion Finding Vertical Initial Velocity (y) Finding Vertical Initial Velocity (y)

17. Vertical Motion Vertical motion will initially have a velocity then accelerate negatively until it stops momentarily, then positively accelerates. Vertical motion will initially have a velocity then accelerate negatively until it stops momentarily, then positively accelerates.

18. Horizontal Motion Finding Horizontal Initial Velocity (x) Finding Horizontal Initial Velocity (x) Horizontal velocity remains constant because it is not being accelerated. Horizontal velocity remains constant because it is not being accelerated.

19. Time “Cut it in half...” “Cut it in half...”

20. Vertical Displacement (y) How High? How High? “Cut it in half...” “Cut it in half...”

21. Horizontal Displacement (x) Horizontal velocity remains CONSTANT Horizontal velocity remains CONSTANT d x = v ix t + 1/2at 2 d x = v ix t t = from start to finish