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Projectile Motion. Projectile. An object that moves through the air only under the influence of gravity after an initial thrust For simplicity , we’ll use 9.8 m/s 2 for gravity. Trajectory – path of a projectile.

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Projectile
Projectile

  • An object that moves through the air only under the influence of gravity after an initial thrust

  • For simplicity, we’ll use

    9.8 m/s2 for gravity.

  • Trajectory – path of a projectile


Projectile motion


Video break
Video Break independent of each other

  • Mythbusters


Force vectors for projectiles
Force vectors for projectiles independent of each other

  • Draw both horizontal and vertical vectors


Vertical horizontal

Vertical independent of each otherHorizontal

d = Vt

V = d/t

d = ½ gt2

V = gt


Horizontally launched cannonball
Horizontally launched cannonball independent of each other


Non horizontally launched cannonball
Non-horizontally launched cannonball independent of each other


Vertical component
Vertical Component independent of each other

  • 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


Horizontal component
Horizontal Component independent of each other

  • Distance

    • d = Vt

  • Velocity

    • V = d/t


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


Example a stone is thrown horizontally at 15 m s from the top of a cliff 44 m high1
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


Example a stone is thrown horizontally at 15 m s from the top of a cliff 44 m high2
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


Example 2 a ball is thrown at a horizontal speed of 18 m s it s flight time is 4 6 seconds
Example 2) A ball is thrown at a horizontal speed of 18 m/s. It’s 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


Example 2 a ball is thrown at a speed of 18 m s it rises and falls in 4 6 seconds
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


Example 2 a ball is thrown at a speed of 18 m s it rises and falls in 4 6 seconds1
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