Introduction to 2D Projectile Motion

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Introduction to 2D Projectile Motion
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Projectile Motion

• An example of 2-dimensional motion.
• Something is fired, thrown, shot, or hurled near
  the earths surface.
• Horizontal velocity is constant.
• Vertical velocity is accelerated.
• Air resistance is ignored.

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Trajectory of Projectile

• This projectile is launched an an angle and rises
  to a peak before falling back down.

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Trajectory of Projectile

• The trajectory of such a projectile is defined by
  a parabola.

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Trajectory of Projectile
Range

• The RANGE of the projectile is how far it travels
  horizontally.

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Trajectory of Projectile
Maximum Height
Range

• The MAXIMUM HEIGHT of the projectile occurs
  halfway through its range.

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Trajectory of Projectile

• Acceleration points down at 9.8 m/s2 for the
  entire trajectory.

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Position graphs for 2-D projectiles
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To work projectile problems

• you must first resolve the initial velocity into
  components.

Vo
?
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Trajectory of Projectile
v
v
v
vo
vf

• Velocity is tangent to the path for the entire
  trajectory.

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Trajectory of Projectile
vx
vx
vy
vy
vx
vy
vx
vy
vx

• The velocity can be resolved into components all
  along its path.

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Trajectory of Projectile
vx
vx
vy
vy
vx
vy
vx
vy
vx

• Notice how the vertical velocity changes while
  the horizontal velocity remains constant.

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Trajectory of Projectile
vx
vx
vy
vy
vx
vy
vx
vx
vy

• Where is there no vertical velocity?

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Trajectory of Projectile
vx
vx
vy
vy
vx
vy
vx
vx
vy

• Where is the total velocity maximum?

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2D Motion

• Resolve vector into components.
• Position, velocity or acceleration
• Work as two one-dimensional problems.
• Each dimension can obey different equations of
  motion.

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Horizontal Component of Velocity
Newton's 1st Law

• Is constant
• Not accelerated
• Not influence by gravity
• Follows equation
• x Vo,xt

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Horizontal Component of Velocity
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Vertical Component of Velocity
Newton's 2nd Law

• Undergoes accelerated motion
• Accelerated by gravity (9.8 m/s2 down)
• Vy Vo,y - gt
• y yo Vo,yt - 1/2gt2
• Vy2 Vo,y2 - 2g(y yo)

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Horizontal and Vertical
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Horizontal and Vertical
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Launch angle
Zero launch angle
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Launch angle
Positive launch angle
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Symmetry in Projectile Motion
Launch and Landing Velocity
Negligible air resistance
Projectile fired over level ground
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Symmetry in Projectile Motion
Time of flight
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Symmetry in Projectile Motion
Time of flight
Projectile fired over level ground
Negligible air resistance