Linear Motion
v ≡
d�t
a ≡
Δv�t
d = v·t
Definition of Average Velocity�(The rate POSITION CHANGES)
Definition of Acceleration�(The rate VELOCITY CHANGES)
Instantaneous Final Velocity�when Accelerating�(How FAST?)
Distance Traveled�when Accelerating�(How FAR?)
Projectile�Motion
Clifton Bluhm
Know the key concept behind Two Dimensional Motion .
Be prepared to do the�“Bull’s Eye LAB”�Next Block Day!!!
I can . . .
Which Bullet Lands First?
Dropped or Shot
Which Bullet Lands First?
Dropped or Shot
Which Bullet Lands First?
Dropped or Shot
Ball Dropped Versus Ball Shot
Demonstration
Horizontal motion is CONSTANT!�
Vertical motion is ACCELERATING
y
y
y
y
y
y
y
No Gravity, But Does Have Horizontal Velocity
velocity is same everywhere!�d = v · t
y
y
y
y
y
y
y
Gravity, AND Horizontal Velocity
.
Projectile Motion
Throw a ball into the air!
Gravity, AND Horizontal Velocity
Gravity, AND Horizontal Velocity
POSITION
y
y
y
y
VELOCITY
y
y
y
VELOCITY
V
Vy0
Vx0
AP Physics 1
y
y
y
y
y
y
y
y
x
y0
x0
vy0
vx0
v
θ
vx = constant
x = x0 + vx0 ∙t
Horizontal
vy = vy0 + g∙t
y = y0 + vy0 ∙t + ½g∙t2
Vertical
(x,y)
y
x
y0
x0
vy0
vxi
v
θ
vyo
vxo
vo
Honors Physics
vx = constant
x = xo + vxo∙t
Horizontal
vy = vyo + g∙t
y = yo + vyo∙t + ½g∙t2
Vertical
?
10.0 m
2.5 m
vx = 1.8 m/s
dy = ½ a · t2
10.0 = ½ 9.80 · t2
t = 1.41 seconds
dx = vx · t
2.5 = vx · 1.41
If the bridge is 18.0 meters off of the water, and the car is traveling at 32.0 m/s, how far horizontally will the car travel before it hits the water?
18.0 m
?
0 = 18.0 + (0)t + ½(-9.80)t2
t = 1.92 seconds
x = 0 + 32.0·1.92
x = 61.3 meters
y
y
y
y
0 = 14.0 + (0)t + ½(-9.80)t2
t = 1.69 seconds
x = 0 + 27.0·1.69
x = 45.6 meters
y
y
y
y
?
14.0 m
27.0 m/s
http://petsports.vstore.ca/product_info.php/products_id/164
http://www.siue.edu/ALUMNI/alumni_target.html
58.0 m
Vx = 175 m/s
dy = ½ a · t2
dy = ½(9.80)(.331)2
t = 58.0 / 175
t = .331 s
dx = vx · t
t = dx / vx
dy = .538 m
dy = .538 m
37°
50 m/s
d = ½·a·t2
d = ½·10·t2
t d
1 s 5 m
2 s 20 m
3 s 45 m
4 s 80 m
5 s 125 m
40 m/s
30 m/s
How far will the object land downrange?
d = 40 m/s · 6 s
d = 240 m
http://petsports.vstore.ca/product_info.php/products_id/164
http://www.siue.edu/ALUMNI/alumni_target.html
(58.0, y)
175 m/s
82.158
154.52
y
y
y
y
58.0 = 0 + 154.52·t
y = 0+ 82.158(.375) + ½(-9.80)(.375)2
t = .375 seconds
y = 30.14 meters
28°
10 ft
40 ft
A kangaroo can jump 40 ft horizontally and 10 ft vertically. How fast is it running?
dy = ½ a · t2
10 = ½(32.2)(t)2
t = .79 s
tair= 2(.79) = 1.6 s
dx = vx · t
40 = vx · 1.6
vx = 25 ft/s
Robbie Maddison – 120 ft Arc de Triomphe, Las Vegas 2008
Robbie Maddison – 120 ft Arc de Triomphe 2008
3.27 seconds of AIR!
322 ft (98.1 meters)
28.1°
34.0 m/s
30.0 m/s
16.0 m/s
Vy = a·t
Vy = 9.80·1.64
tup = 1.64 s
ttotal = 3.27 s
dx = Vx· t
Vx = 30.0 m/s
98.1 = Vx · 3.27
98.1 meters
76.1 mi/hr
Vy = 16.0 m/s
V = √16.02 + 30.02
V = 34.0 m/s
?
?
tan(?) = 16.0/30.0
? = 28.1
dy= ½ a·t2
dy= ½ 9.80·1.642
dy= 13.1 m
dy= 43.1 ft
d = ½ a·t2
= ½ 9.80·(1 sec)2
LASER
4.90 m
8 km
= 4.90 m
Light
Amplification by the
Stimulated
Emission of
Radiation
4.90 m
?
? = 7,901 m
6,371,020 m
6,371,020 m
? = √(6,371,020 + 4.90)2 – 6,371,0202
30 m/s
30 m/s
28.2 m/s
28.2 m/s
10.3 m/s
10.3 m/s
20°
70°
Hang Time = 2.09 seconds
Hang Time = 5.64 seconds
dx = Vx · t
dx = 10.3 · 5.64
dx = 58.1 m
dx = Vx · t
dx = 58.1 m
dx = 28.2 · 2.06
V0 m/s
V0cos(θ)
V0sin(θ)
θ
V0 m/s
V0sin(90-θ)
V0cos(90- θ)
(90- θ)
-V0sin(θ) = V0sin(θ) - 9.8∙t
-2V0sin(θ) = -9.8∙t
2∙V0sin(θ) / 9.8 = t
x = 0 + V0cos(θ)∙t
x = V0cos(θ)∙ 2V0sin(θ) / 9.8
x = 2∙V02cos(θ)∙sin(θ) / 9.8
x = 2∙V02cos(90-θ)∙sin(90-θ) / 9.8
x = 2∙V02sin(θ)∙cos(θ) / 9.8
cos(90-θ) = sin(θ)
sin(90-θ) = cos(θ)
http://www.novanewsnow.com/imgs/dynamique/articles/gros/track.jpg
45°
http://4.bp.blogspot.com/_9T2cRtlgHV0/SKrMTJYz1UI/AAAAAAAAAls/Q0LQAdwYzkk/s400/Women%27s-Javelin-Throw-Mikaela-Ingberg.jpg
http://www.iaaf.net/mm/photo/competitions/competition/04/77/03/47703_full-lnd.jpg
I can . . .