Linear and Non Linear Motion. Reading: Supplemental Textbook Materials, pages

Transcription

1 Linear and Non Linear Motion Reading: Supplemental Textbook Materials, pages 73-87

2 Acceleration Rate of increase of a rate d/t t Increases rate for each increment in time that has passed So there is an increased of distance for each successive time interval

3 Distance g= acceleration of gravity (a)= 10m/s t lower case for time (T upper case means Temperature) 1 gt d = d = t 1 10 ( s m )

4 Distance d=vt? Average velocity V a =(V i +V f )/ d = d= [(v i +v f )/]t v=at or v=gt Substitute this v into d=vt d= [(v i +v f )/]t, with v i =0 1 gt d = 1 gt

5 Distance Traveled Time elapsed Speed 0 0 m/s 1 10 m/s 0 m/s 3 30 m/s 4 40 m/s Distance traveled in 1 second 0 5 m 15 m 5 m 35 m Total Distance traveled 0 m 5 m 0 m 45 m 80 m

6 Problem Cat steps off ledge and reaches ground after ½ second. How fast was she going when she touched the ground? What is the height of the ledge? v = gt 1 d = gt

7 Equations How fast? v = gt How far? d = 1 gt

8 Cat s jump how fast? 10m v = ( )0. 5s s 10m v = ( )0.5s = 5m / s s

9 Cat s jump how far? d = 1 10m ( )(0.5s) s 1 10m d = ( )(0.5s ) = 1. 5m s

10 Basketball Player Hangtime Spud Webb had 1.5 m vertical jump How long could he stay in the air? d = 1 gt (1.5m) d 10m t =, g = t = = 0. 5s g s 10m s

11 Acceleration Rate of increase of a rate d/t t Increases rate for each increment in time that has passed So there is an increased of distance for each successive time interval

12 Relative Motion With respect to another object Earth moving 30 km/s Airplane has airspeed There is windspeed Influences groundspeed

13 Relative Motion Airplane flies 100 mi./h Wind blowing 0 mi./h Same direction simple adding Opposite direction subtract Differing directions draw to scale or solve

14 Diagonal speeds Vector has magnitude and direction Resultant Vector-- Add the two Same direction simple adding Opposite direction subtract Differing directions draw to scale or solve

15 Solving Diagonal Vectors Use Pythagorean theorem a + b = c works for lengths of legs of right triangles a c b

16 Diagonal Vectors Draw rectangle of components a and b Draw diagonal of rectangle Legs on right angle are a and b Diagonal is c a c b

17 Diagonal Vectors Boat traveling 8 km/h b Crossing river flowing 6 km/h a What is boat s speed across river? c c a b

18 Diagonal Vectors Boat traveling 8 km/h b =64 Crossing river flowing 6 km/h a =36 What is boat s speed across river? c c= = 100 = 10km / h a b

19 Types of Motion Linear in a straight line Non-linear curved path Projectiles have curved path called parabola Parabolic curves are parabolas

20 Projectiles Move both horizontally and vertically Vertical motion influenced by gravity Horizontal motion not influenced by gravity Are NOT dependent upon one another

21 Roll the Ball Freely falling object Has acceleration downward Pushed away from table Has velocity outward Combines to have a parabolic path

22 Path of Ball from Side Ball Rolling off table horizontal vertical

23 Top View of the ball Top View Series distance from table

24 Front View the ball Front View

25 Projectile motion Each component acts separately Same horizontal distance in each time increment Vertical distance increases for each time increment that passes

26 Path of Ball from Side Ball Rolling off table horizontal vertical

27 What if?? What if you were at a level shooting range, and dropped a bullet from your hand at exactly the instant a shooter fired a bullet at a paper target 1000 meters away? Which bullet would hit the ground first?

28 350 Cannon Ball Trajectory with no Gravity 300 Vertical height Horizontal distance

29 Cannonball with Gravity Vertical Height Horizontal Distance

30 Faster Cannonball Height Distance

31 How Fast is it going? Horizontal Speed does not change Vertical speed function of time How fast was it going up to begin with This changes due to acceleration of gravity v 0 v = gt v ± v 0 change

32 Steeper Cannonball Vertical Horizontal

33 Acceleration of Cannonball Cannonball What is the acceleration in a horizontal direction? Vertical Horizontal

34 Acceleration of Cannonball Cannonball What is the acceleration in a vertical direction? Vertical Horizontal

35 Cannonball Trajectories

36 Cannonball trajectories Projectile will fall from maximum height in same amount of time it took to rise Because the acceleration of gravity slows it at the same rate it increases the speed on the way down