Linear Kinematic Quantities
How do we define kinematics?
Chapter 10
Linear Kinematics of
Human Movement
© 2007 McGraw-Hill Higher Education. All rights reserved.
• the form, pattern, or sequencing of
movement with respect to time
• the appearance of a motion
© 2007 McGraw-Hill Higher Education. All rights reserved.
Linear Kinematic Quantities
Linear Kinematic Quantities
What is linear displacement?
• change in location
Finish
• the directed distance from initial to final
location
• the vector equivalent of linear distance
• measured in units of cm, m, km
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Start
The distance a skater travels may be measured
from the track left on the ice. The skater’s
displacement is measured in a straight line from
start to finish.
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Linear Kinematic Quantities
Linear Kinematic Quantities
What is linear velocity?
Current
velocity
• the rate of change in location
displacement
• velocity =
time
d
v=t
• the vector equivalent of linear speed
m
• measured in units of s
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Swimmer’s
velocity
Resultant
velocity
The velocity of a swimmer in a river is the vector
sum of the velocities of swimmer and current.
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Linear Kinematic Quantities
Linear Kinematic Quantities
What is acceleration?
Increasing velocity
Increasing velocity
• the rate of change in linear velocity
change in velocity
• acceleration =
time
v2-v1
•
a= t
m
• measured in units of s
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Kinematics of Projectile Motion
What is a projectile?
(a body in free fall that is subject only to
the forces of gravity and air
resistance)
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Kinematics of Projectile Motion
Two balls - one dropped and one projected horizontally
from the same height:
Positive acceleration
Negative acceleration
Decreasing velocity
Decreasing velocity
Negative acceleration
Positive acceleration
Motion in a negative direction
Motion in a positive direction
Acceleration may be positive, negative, or
equal to zero, based on the direction of motion
and the direction of the change in velocity.
© 2007 McGraw-Hill Higher Education. All rights reserved.
Kinematics of Projectile Motion
Why do we analyze the horizontal and
vertical components of projectile motion
separately?
(the vertical component is influenced
by gravity and the horizontal
component is not)
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Kinematics of Projectile Motion
What is the effect of gravity?
(The force of gravity produces a
constant acceleration of -9.81 m/s2
on bodies near the surface of the
earth.)
Both land at the same time since gravity affects their
vertical velocities equally.
© 2007 McGraw-Hill Higher Education. All rights reserved.
© 2007 McGraw-Hill Higher Education. All rights reserved.
2
Kinematics of Projectile Motion
apex
The pattern of
change in the
vertical
velocity of a
projectile is
symmetrical
about the
apex.
Vertical velocity
decreases as the
ball rises and
increases as the
ball falls due to
the influence of
gravitational
force.
gravity
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Maximum height (m)
Factors Influencing Projectile
Trajectory
The Effect of Projection Angle on Range
(Relative Projection Height = 0)
Projection
Projection
Speed
Angle
Range
(m/s)
(degrees)
(m)
5
4
3
2
1
0
0
1
2
3
4
5
6
7 8
9 10 11
Range (distance) (m)
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Factors Influencing Projectile
Trajectory
What factors influence the trajectory
(flight path) of a projectile?
• projection speed - the magnitude of
projection velocity
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What factors influence the trajectory
(flight path) of a projectile?
• projection angle - the direction of
projection with respect to the
horizontal
© 2007 McGraw-Hill Higher Education. All rights reserved.
Factors Influencing Projectile
Trajectory
This scaled
diagram shows
the size and
shape of
trajectories for
an object
projected at 10
m/s at different
angles.
Factors Influencing Projectile
Trajectory
10
10
10
10
10
10
10
10
10
10
20
30
40
45
50
60
70
80
3.49
6.55
8.83
10.04
10.19
10.04
8.83
6.55
3.49
© 2007 McGraw-Hill Higher Education. All rights reserved.
Factors Influencing Projectile
Trajectory
What factors influence the trajectory
(flight path) of a projectile?
• relative projection height - the
difference between projection height
and landing height
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3
Factors Influencing Projectile
Trajectory
FACTORS INFLUENCING PROJECTILE MOTION
(Neglecting Air Resistance)
Variable
Factors of Influence
Initial vertical velocity
Flight time
Relative projection height
Horizontal velocity
Horizontal displacement
Initial vertical velocity
Vertical displacement
Relative projection height
Initial vertical velocity
Relative projection height
Trajectory
Initial speed
Projection angle
Relative projection height
© 2007 McGraw-Hill Higher Education. All rights reserved.
Analyzing Projectile Motion
The Equations of Constant Acceleration
v2 = v1 + at
(1)
d = v1t + ½ at2
(2)
v22 = v12 + 2ad
(3)
These equations may be used to relate linear
kinematic quantities whenever acceleration (a) is
a constant, unchanging value.
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