Kinematics: Projectile Motion

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Kinematics Projectile Motion

• What is Projectile Motion?
• Characteristics of a Projectiles Trajectory
• Horizontal and Vertical Velocity
• Horizontal and Vertical Displacement

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Projectile Motion

• Projectile motion refers to the motion of an
  object projected into the air at an angle.
• Eg. A soccer ball begin kicked, a baseball begin
  thrown, or an athlete long jumping
• The motion that acts vertically is the force of
  gravity, and this pulls an object towards the
  earth at 9.81 m/s2.
• The motion is also moving horizontally but the
  motion is uniform and constant.
• The path of any projectile is a parabola.

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Horizontal Motion Vertical Motion
Forces No Yes, the force of gravity acts downward
Acceleration No Yes , "g" is downward at 9.81 m/s2
Velocity Constant Changing (each second the velocity is increasing by 9.81 m/s)
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The two motions are independent to each other.

• So an object projected horizontally will reach
  the ground in the same time as an object dropped
  vertically. No matter how large the horizontal
  velocity is, the downward pull of gravity is
  always the same.

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Formulas

• Vertical Velocity
• v2y v1y ay?t v1y (-9.81m/s2)?t
• Vertical Displacement
• ?dy v1yi?t 1 ay?t2 v1y?t 1 (-9.81m/s2) ?t2
• 2 2
• Horizontal Velocity
• vx v1x
• Horizontal Displacement
• ?dx vx?t

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Problem Type 1 No initial vertical velocity (vy1
0.0m/s) Once the object leaves the table, it
experiences a downward acceleration equal to
gravity. Thus the vertical velocity(vy)
iscontinually increasing. The horizontal
velocity(vx) remains constant and is equal to
vx0. The two vectors vx and vy are added
together to get the velocity at each point on the
path.
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• Problem Type 2 The projectile is launched at an
  angle
• If an object is pointed at an angle, the motion
  is essentially the same except that there is now
  an initial vertical velocity(vy0). Because of the
  downward acceleration of gravity, vy continually
  decreases until it reaches its highest point, at
  which it begins to fall downward.
• Initial vertical velocity is equal to vy1
  v1(sin?)
• Initial horizontal velocity is equal to vx1
  v1(cos?)

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Problem Type 1 No initial vertical velocity (vy1
0.0m/s)

• A pool ball leaves a 0.60-meter high table with
  an initial horizontal velocity of 2.4 m/s.
  Predict the time required for the pool ball to
  fall to the ground and the horizontal distance
  between the table's edge and the ball's landing
  location.
• A soccer ball is kicked horizontally off a
  22.0-meter high hill and lands a distance of 35.0
  meters from the edge of the hill. Determine the
  initial horizontal velocity of the soccer ball.

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Problem Type 2 The projectile is launched at an
angle

• 3. A long jumper leaves the ground with an
  initial velocity of 12 m/s at an angle of
  28-degrees above the horizontal. Determine the
  time of flight, the horizontal distance, and the
  peak height of the long-jumper.