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Chapter 10: Linear Kinematics of Human Movement

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Horizontal velocity is necessary to carry jumper over bar into pit. Typical takeoff velocity for elite high jumpers is approximately 45 Goals for Projectiles ... – PowerPoint PPT presentation

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Title: Chapter 10: Linear Kinematics of Human Movement


1
Chapter 10Linear Kinematics of Human Movement
  • Basic Biomechanics, 4th edition
  • Susan J. Hall
  • Presentation Created by
  • TK Koesterer, Ph.D., ATC
  • Humboldt State University

2
Objectives
  • Discuss the interrelationship among kinematic
    variables
  • Correctly associate linear kinematic quantities
    with their units of measure
  • Identify describe effects of factors governing
    projectile trajectory
  • Explain why the horizontal and vertical
    components of projectile motion are analyzed
    separately
  • Distinguish between average instantaneous
    quantities identify circumstance which each is
    a quantity of interest

3
Linear Kinematic Quantities
  • Kinematics describes appearance of motion
  • Kinetics study of forces associated with motion
  • Linear kinematics involves the study of the
    shape, form, pattern and sequencing of linear
    movement through time
  • Qualitative major joint actions sequencing
  • Quantitative Range of motion, forces, distance
    etc.

4
Distance Displacement
  • Measured in units of length
  • Metric meter, kilometer, centimeter, etc.
  • English inch, foot, yard mile
  • Distance
  • Scalar quantity
  • Linear displacement
  • Vector quantity length direction (compass
    directions, left, right, up, down, or positive
    negative

5
Speed Velocity
  • Speed length (or distance)
  • change in time
  • Velocity (v) change in position ? position
  • change in time
    ? time
  • v displacement d
  • change in time ? t

6
Speed Velocity
  • Velocity position2 - position1
  • time2 - time1
  • Velocity is a vector quantity
  • direction and magnitude of motion
  • Laws of vector algebra

7
10-2
8
Acceleration
  • Acceleration (a) change in velocity ?v
  • change in time
    ?t
  • a v2 - v1
  • ?t
  • When acceleration is zero, velocity is constant

9
Positive/Negative Acceleration
10
Average Instantaneous Quantities
  • Instantaneous
  • Instantaneous values
  • Average
  • Average velocity final displacement
  • total
    time

11
Velocity Curve for Sprinting
12
Velocity Curves for Two Sprinters
13
Kinematics of Projectile Motion
  • Bodies projected into the air are projectiles
  • Horizontal Vertical Components
  • Vertical is influenced by gravity
  • No force (neglecting air resistance) affects the
    horizontal
  • Horizontal relates to distance
  • Vertical relates to maximum height achieved

14
Kinematics of Projectile Motion Influence of
Gravity
  • Major influence of vertical component
  • Not the horizontal component
  • Force of Gravity
  • Constant, unchanging
  • Negative acceleration (-9.81 m/s2)
  • Apex
  • The highest point in the trajectory

15
10-6
16
Kinematics of Projectile Motion Influence of Air
Resistance
  • In a vacuum, horizontal speed of a projectile
    remain constant
  • Air resistance affects the horizontal speed of a
    projectile
  • This chapter, velocity will be regarded as
    constant

17
Factors Influencing Projectile Trajectory
  • Trajectory
  • Angle of projection
  • Projection speed
  • Relative height of projection

18
10-9
19
Factors Influencing Projectile Trajectory
  • Angle of Projection
  • General shapes
  • Perfectly vertical
  • Parabolic
  • Perfectly horizontal
  • Implications in sports
  • Air resistance may cause irregularities

20
10-10
21
Factors Influencing Projectile Trajectory
  • Projection speed
  • Range
  • Relative Projection Height

22
10-14
23
Optimum Projection Conditions
  • Maximize the speed of projection
  • Maximize release height
  • Optimum angle of projection
  • Release height 0, then angle 450
  • ? Release height, then ? angle
  • ? Release height, then ? angle

24
Range at Various Angles
25
Analyzing Projectile Motion
  • Initial velocity
  • Horizontal component is constant
  • Horizontal acceleration 0
  • Vertical component is constantly changing
  • Vertical acceleration -9.81 m/s2

26
10-17
27
Equations of Constant Acceleration
  • Galileos Laws of constant acceleration
  • v2 v1 at
  • D v1t ½at2
  • V22 v21 2 ad
  • d displacement v velocity
  • a acceleration t time
  • Subscript 1 2 represent first or initial and
    second or final point in time

28
Equations of Constant Acceleration
  • Horizontal component a 0
  • v2 v1
  • D v1t
  • V22 v21

29
Equations of Constant Acceleration
  • Vertical component a -9.81 m/s2
  • v2 at
  • D ½ at2
  • V22 2ad
  • Vertical component at apex v 0
  • 0 v21 2ad
  • 0 v1 at

30
Goals for Projectiles
  • Maximize range (shot put, long jump)
  • Maximize total distance (golf)
  • Optimize range and flight time (punt)
  • Maximize height (vertical jump)
  • Optimize height and range (high jump)
  • Minimize flight time (baseball throw)
  • Accuracy (basketball shot)

31
Goals for Projectiles
  • Maximize range (shot put, long jump)
  • Shot put optimum angle is approximately 42
  • Long jump theoretical optimum is approximately
    43 however, due to human limits, the actual
    angle for elite jumpers is approximately 20 - 22

32
Goals for Projectiles
  • Maximize total distance (golf)
  • Because the total distance (flight plus roll) is
    most important, trajectory angles are lower than
    45
  • Distance is controlled by the pitch of the club
  • Driver 10

33
Goals for Projectiles
  • Optimize range and flight time (punt)
  • Maximum range occurs with 45 trajectory
  • Higher trajectory increases hang time with
    minimal sacrifice in distance
  • Lower trajectory usually results in longer punt
    returns
  • Less time for kicking team to get downfield to
    cover the punt returner

34
Goals for Projectiles
  • Maximize height (vertical jump)
  • Maximize height of COM at takeoff
  • Maximize vertical velocity by exerting maximum
    vertical force against ground.

35
Goals for Projectiles
  • Optimize height and range (high jump)
  • Basic goal is to clear maximum height
  • Horizontal velocity is necessary to carry jumper
    over bar into pit
  • Typical takeoff velocity for elite high jumpers
    is approximately 45

36
Goals for Projectiles
  • Minimize flight time (baseball throw)
  • Baseball players use low trajectories (close to
    horizontal)
  • Outfielders often throw the ball on one bounce
    with minimal loss of velocity

37
Goals for Projectiles
  • Accuracy (basketball shot)

38
Projecting for Accuracy
39
Minimum Speed Trajectory
40
Angle of Entry
41
Margin for Error
42
Free Throw Optimum Angle
43
Summary
  • Linear kinematics is the study of the form or
    sequencing of linear motion with respect to time.
  • Linear kinematic quantities include the scalar
    quantities of distance and speed, and the vector
    quantities of displacement, velocity, and
    acceleration.
  • Vector quantities or scalar equivalent may be
    either an instantaneous or an average quantity

44
Summary
  • A projectile is a body in free fall that is
    affected only by gravity and air resistance.
  • Projectile motion is analyzed in terms of its
    horizontal and vertical components.
  • Vertical is affected by gravity
  • Factors that determine the height distance of a
    projectile are projection angle, projection
    speed, and relative projection height
  • The equation for constant acceleration can be
    used to quantitatively analyze projectile motion.

45
The End
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