PROJECTILE MOTION

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PROJECTILE MOTION
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Projected vs Dropped

• Both balls will hit the ground at the same time
  whether dropped vertically or fired horizontally,
  bc gravity is the force that is pulling on them
  equally downward. If the one being fired is fired
  at a higher height then the only difference is
  that it will land father than the previous time
  it was launched.

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Formulas

• ?x1/2(ViVf)t
• ?xVit1/2at²
• VfViat
• Vf2Vi²2a?x

Time is the connecting factor b/t horizontal and
vertical motion
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Problem Solving Steps

• Draw Picture
• Write Knowns
• Identify Unknowns
• Choose Write equation to be used
• Simp. Eq. by eliminating terms0
• Solve Eq. in terms of variables
• Plug in s solve for Unknown
• Ans. Given question check ans.

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Problem 1

• The ball that was thrown horizontally from a
  cliff at a height of 25m and lands 8m from the
  base of the cliff. How fast was the ball going?

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SOLVE

• ?xvVivtv1/2avtv²
• T v(?x/.5a)
• T v(25m/(9.8/2))
• T 2.59s
• --------------------------------
• Vi ?xh/(.5ahth²th) ah0
• Vi ?x/t
• Vi 8m/2.59
• Vi 3.54m/s
• The ball was going at 3.54m/s.

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Problem 2

• How far does a bullet land when shot horizontally
  at a height of 2m going at a speed of 20m/s?

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Solve

• ?xvVivtv1/2avtv²
• T v(?x/.5a)
• T v(2m/(9.8/2))
• T .64s
• ------------------------------
• ?xhVihth1/2ahth² a0
• ?xhVihth
• ?xh 20m/s(.64s)
• ?xh 12.8m The ball lands 12.8m away.

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Review Problems

• At the instant a ball is thrown horizontally over
  a level range, a ball held at the side is
  dropped. If air-resistant is neglected which one
  strikes the ground first?
• How far below an initial straight-line path will
  a horizontally fired projectile fall in 1sec?
• Neglecting air resistance if a ball is thrown
  straight up at 20m/s, how fast will it be moving
  when you catch it?
• At what point in the projectile speed is it at
  its minimum?

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Answers

• Both will hit at the same time.
• 4.9m
• 20m/s
• At the top of its path where its changing
  direction.