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Projectile Motion

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Projectile Motion

- 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

- 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.

- Mythbusters

- Draw both horizontal and vertical vectors

VerticalHorizontal

d = Vt

V = d/t

d = ½ gt2

V = gt

- 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

- Distance
- d = Vt

- Velocity
- V = d/t

- 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

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

d

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

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

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

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