# Chapter 10: Linear Kinematics of Human Movement

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13 Νοε 2013 (πριν από 4 χρόνια και 7 μήνες)

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Chapter 10:

Linear Kinematics of
Human Movement
Basic Biomechanics, 4
th
edition
Susan J. Hall
Presentation Created by
TK Koesterer, Ph.D., ATC
Humboldt State University
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
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.
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
Speed & Velocity
Speed = length (or distance)
change in time
Velocity (v) = change in position =
Δ
position
change in time
Δ
time
v = displacement = d
change in time
Δ
t
Speed & Velocity
Velocity = position
2
- position
1

time
2
- time
1

Velocity is a vector quantity

direction and magnitude of motion

Laws of vector algebra
10-2

Acceleration
Acceleration (a) = change in velocity =
Δ
v
change in time
Δ
t

a = v
2
- v
1

Δ
t
When acceleration is zero, velocity is constant
Positive/Negative Acceleration
Average & Instantaneous
Quantities
Instantaneous :

Instantaneous values
Average:

Average velocity = final displacement
total time
Velocity Curve for Sprinting
Velocity Curves for Two Sprinters
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
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/s
2
)
Apex:

The highest point in the trajectory
10-6

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

Factors Influencing
Projectile Trajectory
Trajectory:

Angle of projection

Projection speed

Relative height of projection
10-9

Factors Influencing
Projectile Trajectory
Angle of Projection

General shapes

Perfectly vertical

Parabolic

Perfectly horizontal

Implications in sports

Air resistance may cause irregularities
10-10

Factors Influencing
Projectile Trajectory
Projection speed:

Range:

Relative Projection Height:
10-14

Optimum Projection Conditions

Maximize the speed of projection

Maximize release height

Optimum angle of projection

Release height = 0, then angle = 45
0

Release height, then

angle

Release height, then

angle
Range at Various Angles
Analyzing Projectile Motion
Initial velocity
:

Horizontal component is constant

Horizontal acceleration = 0

Vertical component is constantly changing

Vertical acceleration = -9.81 m/s
2

10-17

Equations of
Constant Acceleration
Galileo’s Laws of constant acceleration
v
2
= v
1
+ at
D = v
1
t + ½at
2

V
2
2
= v
2
1

d = displacement; v = velocity;

a = acceleration; t = time

Subscript 1 & 2 represent first or initial and
second or final point in time
Equations of
Constant Acceleration
Horizontal component : a = 0
v
2
= v
1

D = v
1
t
V
2
2
= v
2
1

Equations of
Constant Acceleration
Vertical component: a = -9.81 m/s
2

v
2
= at
D = ½ at
2

V
2
2

Vertical component at apex: v = 0

0 = v
2
1

0 = v
1
+ at
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)

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°
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
°
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
Goals for Projectiles

Maximize height (vertical jump)

Maximize height of COM at takeoff

Maximize vertical velocity by exerting
maximum vertical force against ground.
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
°

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
Goals for Projectiles

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