Linear and Non Linear MotionAccelerationDistanceDistanceDistance TraveledProblemEquationsCat’s jump—how fast?Cat’s jump—how far?Basketball Player HangtimeAccelerationRelative MotionRelative MotionDiagonal speedsSolving Diagonal VectorsDiagonal VectorsDiagonal VectorsDiagonal VectorsTypes of MotionProjectilesRoll the BallPath of Ball from SideTop View of the ballFront View the ballProjectile motionPath of Ball from SideWhat if??How Fast is it going?Acceleration of CannonballAcceleration of CannonballCannonball TrajectoriesCannonball trajectoriesLinear and Non Linear MotionReading: Supplemental Textbook Materials, pages 273-287Acceleration• Rate of increase of a rated/tt• Increases rate for each increment in time that has passed• So there is an increased of distance for each successive time intervalDistance• g= acceleration of gravity (a)= 10m/s2• t lower case for time• (T upper case means Temperature)221gtd =22)10(21tsmd =Distance• d=vt ?• Average velocityVa=(Vi+Vf)/2• d= [(vi+vf)/2]t• v=at or v=gt• Substitute this v into d=vtd= [(vi+vf)/2]t, with vi=0221gtd =221gtd =Distance TraveledTime elapsedSpeed00 m/s110 m/s220 m/s330 m/s440 m/sDistance traveled in 1 second05 m15 m25 m35 mTotal Distance traveled0 m5 m20 m45 m80 mProblem• 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?gtv=221gtd =Equations•How fast?•How far?gtv=221gtd =Cat’s jump—how fast?ssmv 5.0)10(2=smssmv /55.0)10(2==Cat’s jump—how far?22)5.0)(10(21ssmd =mssmd 25.1)25.0)(10(2122==Basketball Player Hangtime• Spud Webb had “1.25 m”vertical jump• How long could he stay in the air?221gtd =210,2smggdt ==ssmmt 5.010)25.1(22==Acceleration• Rate of increase of a rated/tt• Increases rate for each increment in time that has passed• So there is an increased of distance for each successive time intervalRelative Motion• With respect to another object• Earth moving 30 km/s• Airplane has airspeed• There is windspeed• Influences groundspeedRelative Motion• Airplane flies 100 mi./h• Wind blowing 20 mi./h•Same direction—simple adding•Opposite direction—subtract•Differing directions—draw to scale or solveDiagonal speeds•Vector – has magnitude – and direction• Resultant Vector-- Add the two– Same direction—simple adding– Opposite direction—subtract– Differing directions—draw to scale or solveSolving Diagonal Vectors• Use Pythagorean theorem•a2+ b2= c2• works for lengths of legs of right trianglesabcDiagonal Vectors• Draw rectangle of components a and b• Draw diagonal of rectangle• Legs on right angle are ‘a’ and ‘b’• Diagonal is ‘c’abcDiagonal Vectors• Boat traveling 8 km/h b• Crossing river flowing 6 km/h a• What is boat’s speed across river? cabcDiagonal Vectors• Boat traveling 8 km/h b2=64• Crossing river flowing 6 km/h a2=36• What is boat’s speed across river?c=abchkm/101006436 ==+Types of Motion• Linear—in a straight line• Non-linear—curved path• Projectiles have curved path called “parabola”• Parabolic curves are parabolasProjectiles• Move both horizontally and vertically• Vertical motion influenced by gravity• Horizontal motion not influenced by gravity• Are NOT dependent upon one anotherRoll the Ball• Freely falling object– Has acceleration downward• Pushed away from table– Has velocity outward• Combines to have a parabolic pathPath of Ball from SideBall Rolling off tablehorizontalverticalTop View of the ballTop Viewdistance from tableSeries2Front View the ballFront ViewProjectile motion• Each component acts separately• Same horizontal distance in each time increment• Vertical distance increases for each time increment that passesPath of Ball from SideBall Rolling off tablehorizontalverticalWhat 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?Cannon Ball Trajectory with no Gravity0501001502002503003500 50 100 150 200 250 300 350Horizontal distanceVertical heightCannonball with Gravity01020304050607080900 102030405060708090Horizontal DistanceVertical HeightFaster Cannonball0501001502002503003500 50 100 150 200 250 300 350DistanceHeightHow 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 gravity0vchangevv±0gtv =Steeper Cannonball0501001502002503003500 50 100 150 200 250 300 350HorizontalVerticalAcceleration of Cannonball• What is the acceleration in a horizontal direction?Cannonball01020304050607080900 102030405060708090HorizontalVerticalAcceleration of Cannonball• What is the acceleration in a vertical direction?Cannonball01020304050607080900 102030405060708090HorizontalVerticalCannonball TrajectoriesCannonball 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
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