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# Projectile Motion PowerPoint PPT Presentation

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.

Projectile Motion

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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/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

### Force vectors for projectiles

• Draw both horizontal and vertical vectors

## VerticalHorizontal

d = Vt

V = d/t

d = ½ gt2

V = gt

### 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

• 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.

• 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 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 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.

• 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.

• 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 seconds.

• What is its vertical speed when it hits the ground?

• V = gt

• V = (9.8)(2.3)

• V = 22.54 m/s