6. Motion The symbol “Δ” means “Change in” QuantitySymbolDefinitionUnitsQuantitySymbolDefinitionUnit DistancedmDisplacementdm Speedvd/Δtm/sVelocityvd/Δtm/s AccelerationaΔv/Δtm/s 2 AccelerationaΔv/Δtm/s 2

8. x y

9. Motion Air Hockey There is no friction between the puck and the table surface a = 0

10. Motion Free Fall Tower Drop distance - dd yHeight above base - y 100 m Assumption: No air resistance

11. Motion Air Hockey, Free Fall Tower Revisited d y 100 m Assumption: No air resistanceAssumption: No friction

18. 2D Motion Path Characteristics

19. 2D Motion Path Characteristics * The combined graph of the two independent motions is identical to the actual motion of an object in free fall (projectile) in two dimensions

20. 2D Motion Path Characteristics * The combined graph of the two independent motions is identical to the actual motion of an object in free fall (projectile) in two dimensions * What happens in the vertical direction is independent of what happens in the horizontal direction

21. 2D Motion Path Characteristics * The combined graph of the two independent motions is identical to the actual motion of an object in free fall (projectile) in two dimensions * What happens in the vertical direction is independent of what happens in the horizontal direction * The actual path is mathematically that of a parabola. The path of any projectile in free fall will be that of a parabola

22. 2D Motion Path Characteristics * The combined graph of the two independent motions is identical to the actual motion of an object in free fall (projectile) in two dimensions * What happens in the vertical direction is independent of what happens in the horizontal direction * The actual path is mathematically that of a parabola. The path of any projectile in free fall will be that of a parabola * In General: Vertical drop distance is given by d = ½ a t 2 Horizontal distance is given byx = vt

29. 2D Motion A cannon and a rifle is held so that their barrels are horizontal and the same height above the ground. A marble is held at the same height above the ground. At exactly the same time, the cannon an rifle are fired and the marble is dropped. Which one hits the ground first? A locomotive has a vertical smoke stack. The train moves at a constant velocity. A projectile is fired out of the stack (in a vertical direction). Will the projectile land in front of the train, behind the train, or back in the stack?

34. 2D Motion A person stands at the edge of a cliff which is 5 m high. The person throws a ball (m = 2 kg) horizontally with a speed of 2 m/sec. How far from the base of the cliff does the ball land? ?