Linear and Non Linear Motion Reading: Supplemental Textbook Materials, pages 73-87
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
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 )
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
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
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
Equations How fast? v = gt How far? d = 1 gt
Cat s jump how fast? 10m v = ( )0. 5s s 10m v = ( )0.5s = 5m / s s
Cat s jump how far? d = 1 10m ( )(0.5s) s 1 10m d = ( )(0.5s ) = 1. 5m s
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
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
Relative Motion With respect to another object Earth moving 30 km/s Airplane has airspeed There is windspeed Influences groundspeed
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
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
Solving Diagonal Vectors Use Pythagorean theorem a + b = c works for lengths of legs of right triangles a c b
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
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
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= 36 + 64 = 100 = 10km / h a b
Types of Motion Linear in a straight line Non-linear curved path Projectiles have curved path called parabola Parabolic curves are parabolas
Projectiles Move both horizontally and vertically Vertical motion influenced by gravity Horizontal motion not influenced by gravity Are NOT dependent upon one another
Roll the Ball Freely falling object Has acceleration downward Pushed away from table Has velocity outward Combines to have a parabolic path
Path of Ball from Side Ball Rolling off table horizontal vertical
Top View of the ball Top View Series distance from table
Front View the ball Front View
Projectile motion Each component acts separately Same horizontal distance in each time increment Vertical distance increases for each time increment that passes
Path of Ball from Side Ball Rolling off table horizontal vertical
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?
350 Cannon Ball Trajectory with no Gravity 300 Vertical height 50 00 150 100 50 0 0 50 100 150 00 50 300 350 Horizontal distance
Cannonball with Gravity 90 80 70 Vertical Height 60 50 40 30 0 10 0 0 10 0 30 40 50 60 70 80 90 Horizontal Distance
Faster Cannonball 350 300 50 Height 00 150 100 50 0 0 50 100 150 00 50 300 350 Distance
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
Steeper Cannonball 350 300 50 Vertical 00 150 100 50 0 0 50 100 150 00 50 300 350 Horizontal
Acceleration of Cannonball Cannonball What is the acceleration in a horizontal direction? 90 80 70 60 Vertical 50 40 30 0 10 0 0 10 0 30 40 50 60 70 80 90 Horizontal
Acceleration of Cannonball Cannonball What is the acceleration in a vertical direction? 90 80 70 60 Vertical 50 40 30 0 10 0 0 10 0 30 40 50 60 70 80 90 Horizontal
Cannonball Trajectories
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