Projectile Motion

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Projectile Motion
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Projectile

• An object that moves through the air only under
  the influence of gravity after an initial thrust
• For simplicity, well use
• 9.8 m/s2 for gravity.
• Trajectory path of a projectile

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• The vertical and horizontal components of a
  projectile are independent of each other
• If 1 ball were dropped and another ball launched
  forward from the same height, they would hit the
  ground at the same time.

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Video Break

• Mythbusters

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Force vectors for projectiles

• Draw both horizontal and vertical vectors

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Vertical Horizontal
d Vt V d/t

• d ½ gt2
• V gt

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Horizontally launched cannonball
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Non-horizontally launched cannonball
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Vertical Component

• Distance
• d Vit ½ gt2 Vi is 0, so it cancels!
• d ½ gt2
• Velocity
• Vf Vi gt Vi is 0, so it cancels!
• V gt

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Horizontal Component

• Distance
• d Vt
• Velocity
• V d/t

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Example) A stone is thrown horizontally at 15
m/s from the top of a cliff 44 m high.

• a) How long does it take to fall?
• d ½ gt2
• 44 ½ (9.80)(t2)
• 44 4.90( t2)
• 8.9796 t2
• t 3.0 s

15m/s
44m
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Example) A stone is thrown horizontally at 15
m/s from the top of a cliff 44 m high.

• b) How far from the base of the cliff does it
  land?
• d Vt
• d (15)(3.0)
• d 45 m

d
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Example) A stone is thrown horizontally at 15
m/s from the top of a cliff 44 m high.

• c) What is its vertical speed when it hits the
  ground?
• V gt
• V (9.80)(3.0)
• V 29.4 m/s

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Example 2) A ball is thrown at a horizontal
speed of 18 m/s. Its flight time is 4.6 seconds.

• How high does the ball go?
• d ½ gt2
• d ½ (9.80)(2.32)
• d 25.92 m

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Example 2) A ball is thrown at a speed of 18
m/s. It rises and falls in 4.6 seconds.

• How far away does it land?
• d Vt
• d (18)(4.6)
• d 82.8 m

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Example 2) A ball is thrown at a speed of 18
m/s. It rises and falls in 4.6 seconds.

• What is its vertical speed when it hits the
  ground?
• V gt
• V (9.8)(2.3)
• V 22.54 m/s