Chapter 10: Linear Kinematics of Human Movement

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Chapter 10Linear Kinematics of Human Movement

• Basic Biomechanics, 4th edition
• Susan J. Hall
• Presentation Created by
• TK Koesterer, Ph.D., ATC
• Humboldt State University

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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

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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.

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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

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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

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Speed Velocity

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

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10-2
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Acceleration

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

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Positive/Negative Acceleration
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Average Instantaneous Quantities

• Instantaneous
• Instantaneous values
• Average
• Average velocity final displacement
• total
  time

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Velocity Curve for Sprinting
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Velocity Curves for Two Sprinters
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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

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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

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10-6
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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

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Factors Influencing Projectile Trajectory

• Trajectory
• Angle of projection
• Projection speed
• Relative height of projection

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10-9
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Factors Influencing Projectile Trajectory

• Angle of Projection
• General shapes
• Perfectly vertical
• Parabolic
• Perfectly horizontal
• Implications in sports
• Air resistance may cause irregularities

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10-10
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Factors Influencing Projectile Trajectory

• Projection speed
• Range
• Relative Projection Height

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10-14
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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

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Range at Various Angles
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Analyzing Projectile Motion

• Initial velocity
• Horizontal component is constant
• Horizontal acceleration 0
• Vertical component is constantly changing
• Vertical acceleration -9.81 m/s2

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10-17
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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

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Equations of Constant Acceleration

• Horizontal component a 0
• v2 v1
• D v1t
• V22 v21

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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

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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)

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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

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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

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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

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Goals for Projectiles

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

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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

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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

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Goals for Projectiles

• Accuracy (basketball shot)

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Projecting for Accuracy
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Minimum Speed Trajectory
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Angle of Entry
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Margin for Error
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Free Throw Optimum Angle
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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

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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.

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The End