Slide 1Checklist for TodayThrow a Ball upSpeederChapter 3Important Equations of MotionPosition in 3 dimensionsVelocity in 3 dimensionsProjectile MotionConstant AccelerationKinematics in 3DCheckpoint 1Ball DroppingProjectile MotionProjectile Motion & Frames of ReferenceProjectile MotionMonkey TroublesShooting the Monkey…Shooting the Monkey…Marbles & MathFiring up in the air at an angleFootball PuntChecklist for TodayPhysics 218Alexei SafonovLecture 5: Kinematics in 2-3DChecklist for Today•For the rest of this week:–Be ready for the lab (WebAssign) including pre-labs–Quiz at the recitation on Chapter 2–There was a pre-lecture for today•Many people completed, but not all–A pre-lecture due Wednesday morning•Don’t forget the checkpoints –Homework for Chapter 3 is due Sunday on MP•Coming week recitation quiz will be on Chapter 3Throw a Ball upYou throw a ball upward into the air with initial velocity V0. Calculate:a) The time it takes to reach its highest point (the top). b) Distance from your hand to the topc) Time to go from your hand and come back to your handd) Velocity when it reaches your hande) Time from leaving your hand to reach some random height h.SpeederA speeder passes you (a police officer) sitting by the side of the road and maintains their constant velocity V. You immediately start to move after the speeder from rest with constant acceleration a.•How much time does it take to ram the speeder?•How far do you have to travel to catch the speeder? •What is your final speed?XPolice Officer SpeederChapter 3•Kinematics in Two or Three Dimensions•Projectile Motion•Uniform Circular MotionImportant Equations of MotionIf the acceleration is constantPosition, velocity and Acceleration are vectors. 221000tatv x xtav v Position in 3 dimensionsxzy^j^i^kkˆZ jˆY iˆX R dimensions 3 inorigin the torelative position,our as R WritekˆZ(t) jˆY(t) iˆX(t) (t)R Velocity in 3 dimensionsxzy^j^i^k dtkˆd dtjˆd 0 dtiˆd used have We :Note kˆ(t)zV jˆ(t)yV iˆ(t)xV kˆdtdZ(t) jˆdtdY(t) iˆdtdX(t) dt)kˆZ(t) jˆY(t) iˆd(X(t) dt(t)Rd V then position, theis R If kˆa jˆa iˆa kˆdtdV jˆdtdV iˆdtdV dt)kˆV jˆV iˆd(V dtVd a zyxzyxzxyProjectile MotionThe horizontal and vertical equations of the motion behave independentlyProblem solving:The trick for all these problems is to break them up into the X and Y directions.Constant Acceleration2y210y02x210x0tat v y y tat v x x t a v v tat v r R 022100ta v vta v vy0yyx0xxMechanics Lecture 2, Slide 11Kinematics in 3DCheckpoint 1A) The launched marble hits first.B) The dropped marble hits first.C) They both hit at the same time.DEMOA physics demo launches one marble horizontally while at the same instant dropping a second marble straight down. Which one hits the ground first?Ball Dropping•Analyze Vertical and Horizontal separately!!!•Ay = g (downwards)•Ax = 0–Constant for Both cases!!!Vx = 0 Vx>0Projectile MotionThe horizontal and vertical equations of the motion behave independentlyProblem solving:The trick for all these problems is to break them up into the X and Y directions.Projectile Motion & Frames of ReferenceProjectile MotionHorizontalVerticalBoringMonkey Troubles•You are a vet trying to shoot a tranquilizer dart into a monkey hanging from a branch in a distant tree. You know that the monkey is very nervous, and will let go of the branch and start to fall as soon as your gun goes off. In order to hit the monkey with the dart, where should you point the gun before shooting?Monkey x = xoDartx = vo tShooting the Monkey…221gty 221gty Shooting the Monkey…y = voy t - 1/2 g t 2Still works even if you shoot upwards!y = yo - 1/2 g t 2Dart hits themonkeyMarbles & Math•Prove mathematically that an object projected horizontally will reach the ground at the same time as an object dropped verticallyFiring up in the air at an angleA ball is fired up in the air with velocity Vo and angle Qo. Ignore air friction. The acceleration due to gravity is g pointing down.What is the final velocity here?Football Punt•A football is kicked at angle Q0 with a velocity V0. The ball leaves the punters foot h meters above the ground. –The velocity at the maximum height–How far does it travel, in the X direction, before it hits the ground?–What angle maximizes the distance traveledhChecklist for Today•For the rest of this week:–Be ready for the lab (WebAssign) including pre-labs–Quiz at the recitation on Chapter 3–There was a pre-lecture for today•Many people completed, but not all–A pre-lecture due Wednesday morning•Don’t forget the checkpoints –Homework for Chapter 3 is due Sunday on MP•Coming week recitation quiz will be on Chapter
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