KIN 3309 1nd Edition Lecture 10 Outline of Last Lecture I. Human Movement AnalysisII. Movements Occur Over TimeIII. Important ParametersIV. Velocity (v)V. Velocity (slope)VI. Velocity EstimationVII. Finite DifferentiationVIII. Instantaneous VelocityIX. Average vs. Instantaneous VelocityX. Graphical ExampleXI. Constant VelocityXII. AccelerationXIII. Instantaneous AccelerationXIV. Constant AccelerationXV. IntegrationXVI. Finite IntegrationXVII. ExampleXVIII. Riemann SumXIX. Kinematic AnalysisXX. Gait KinematicsXXI. How to Solve Kinematics ProblemsXXII. QuizOutline of Current Lecture I. What is a Projectile?II. Projectile MotionIII. Factors Influencing ProjectilesIV. Factors Affecting TrajectoryV. Dropping SomethingVI. Equations of MotionVII. Tossing an Object Straight UpThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.VIII. Two DimensionsIX. How Far Will it Go? – Problem X. Two DimensionsXI. Initial Angle – ProblemXII. Range (Flat Ground) – Problem XIII. Range (Uneven Ground) – Problem XIV. QuizCurrent LectureI. What is a Projectile?a. An object that is only acted on by:i. Gravityii. Air resistance (we will ignore today)b. We have no control over the object once we lose contact with itc. Thrown implements (balls, discus, shot) and airborne humans (long jump, high jump) can be projectilesII. Projectile Motiona.b. What do we want to control? i. How far, how long, how highc.III. Factors Influencing Projectilesa. Gravityb. Air resistancei. Air resistance is often negligibleii. Air resistance is considered negligible in this section of the textc. No other forces can influence the flight (trajectory) of the projectileIV. Factors Affecting Trajectorya.V. Dropping Somethinga. E.g., a hockey puck onto the ice.i. What acceleration do we use?ii. What is the initial velocity?iii. What is the initial vertical position?b. The velocity increases as the puck fallsc. Thus, as the puck moves farther from its initial starting position, the faster it goesVI. Equations of Motiona.b.VII. Tossing an Object Straight Upa. Part one – going up…b. Say vi = 2 m/sc. Lets explore by using:i.d. Note that, at some point, v = 0i. What is that point?1. The peak of the trajectory. The highest point of the path.ii. How high does it go?1. ~2/10ths of a meteriii. How long is it in the air?1. ~2/10ths of a seconde. How would we make it go higher?VIII. Two Dimensionsa. Usually, we don’t only care about how high something goesi. Even pole-vaulters and high jumpers don’t go straight up – they have to move forwardb. We usually want something to go a particular distance or as far as possiblei. A free throw, a kick offii. Shot put, long jumpc. Horizontal and vertical components are independentd. The parabolic trajectory of projectilesi. Vertical velocity is zero at peak heightii. Horizontal velocity is unchangediii. Peak height occurs at ½ total horizontal distance, and at ½ total time (when starting and ending at the same height)iv. No new equations!v. Just remember to designate x- and y- variables!1. Also seen as h and v for horizontal and verticalIX. How Far Will it Go? -- Problema. Kick a soccer ball – given the initial the following characteristics:i. 15 m/s horizontal velocity, 10 m/s vertical velocityii.b. Break it into up and down parts of the trajectoryi. Solve for tup using…1.ii. Solve for total time: peak height occurs at ½ total time so…1.iii. Solve for pf using…1.c.X. Two Dimensionsa. The parabolic trajectory of projectilesi. Vertical velocity is zero at peak heightii. Horizontal velocity is unchangediii. Peak height occurs at ½ total horizontal distance, and at ½ total time (when starting and ending at the same height)XI. Initial Anglea. Often you will be given the initial angle (theta) and the total velocity (vtot)i. Instead of the initial horizontal and vertical velocitiesb.c.d. Kick a football at 30 degrees and 30 m/s.i. Calculateii. XII. Range (Flat Ground) – Problem a.b. Kick a soccer ball – given the initial the following characteristics:i. 15 m/s horizontal velocity, 10 m/s vertical velocity1.ii.XIII. Range (Uneven Ground) – Problem a. This time the same football is kicked from the roof of a garage (height 1.76m)b.c.d.e.XIV. Quiza. A valuter is trying to reach a velocity of 7 m/s at the end of 14-m runway. How quickly must he accelerate?i. 0.50 m/s2ii. 1.75 m/s2iii. 2.00 m/s2iv. 3.50 m/s2b. A child’s vertical takeoff velocity when jumping on a trampoline is 5.3 m/s. Assuming takeoff and landing heights are the same, how long is the child airborne?i. 0.29 sii. 0.54 siii. 1.08 siv. 1.85 sc. A shot-putter throws the shot with a horizontal velocity of 10 m/s and a vertical velocity of 10 m/s from a height of 2.0 m. Calculate the range of the throw.i.