Physics 211 Lecture 2, Slide 1

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Physics 211 Lecture 2
Today's Concepts a) Vectors b) Projectile
motion c) Reference frames
Reminder HW, Due-dates, grade cutoffs
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Vectors
Ay
A
Ax
Think of a vector as an arrow. (An object having
both magnitude and direction)
The object is the same no matter how we chose to
describe it
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3
Vectors
A
A
q
Think of a vector as an arrow. (An object having
both magnitude and direction)
The object is the same no matter how we chose to
describe it
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4
Vector Addition
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5
ACT
Vectors and are shown to the right.
Which of the following best describes
A B C D
E
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6
ACT
Vectors and are shown to the right.
Which of the following best describes -
A B C D
E
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ACT
Vectors and are shown to the right.
Which of the following best describes
A B C D
E
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8
Vectors in 3D
A vector can be defined in 2 or 3 (or even more)
dimensions
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Kinematics in 3D
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10
A physics demo launches one marble horizontally
while at the same instant dropping a second
marble straight down. Which one hits the ground
first?
Preflight 1
A) The launched marble hits first. B) The dropped
marble hits first. C) They both hit at the same
time
DEMO
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Projectile Motion
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Train Demo Act
A flatbed railroad car is moving along a track at
constant velocity. A passenger at the center of
the car throws a ball straight up. Neglecting
air resistance, where will the ball land? A.
Forward of the center of the car B. At the center
of the car C. Backward of the center of the car
x- direction Ball and car start with same
position and velocity, a0, so always have same
position
Demo - train
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Monkey Troubles

• You are a vet trying to shoot a tranquilizer dart
  into a monkey hanging from a branch in a distant
  tree. You know that the monkey is very nervous,
  and will let go of the branch and start to fall
  as soon as your gun goes off. In order to hit the
  monkey with the dart, where should you point the
  gun before shooting?
• A Right at the monkey
• B Below the monkey
• C Above the monkey

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Shooting the Monkey...
Dart x v0 t y -1/2 g t2
Monkey x x0 y -1/2 g t2
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Shooting the Monkey...
y y0 - 1/2 g t2

• Still works even if you shoot upwards!

y v0y t - 1/2 g t2
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Projectile Motion Frames of Reference
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A destroyer simultaneously fires two shells with
the same initial speed at enemy ships. If the
shells follow the parabolic trajectories shown,
which ship gets hit first?
ACT (Preflight 2)
Enemy 1
Enemy 2
Destroyer
A) Enemy 1 B) Enemy 2 C) They are both hit at the
same time
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A destroyer simultaneously fires two shells with
the same initial speed at enemy ships. If the
shells follow the parabolic trajectories shown,
which ship gets hit first?
Preflight 2
Enemy 1
Enemy 2
Destroyer
A) Enemy 1 B) Enemy 2 C) They are both hit at the
same time
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A battleship simultaneously fires two shells with
different initial speeds at enemy ships. If the
shells follow the parabolic trajectories with
same maximum height as shown below, which ship
gets hit first?
ACT (Preflight 3)
Enemy 1
Enemy 2
Destroyer

• A) Enemy 1
• B) Enemy 2
• C) They are both hit at the same time

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21
A battleship simultaneously fires two shells with
different initial speeds at enemy ships. If the
shells follow the parabolic trajectories with
same maximum height as shown below, which ship
gets hit first?
Preflight 3
Enemy 1
Enemy 2
Destroyer

• A) Enemy 1
• B) Enemy 2
• C) They are both hit at the same time

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Field Goal Example

• Our field goal kicker can kick the ball 30 m/s at
  an angle of 30 degrees w.r.t. the ground. If the
  crossbar of the goal post is 3m off the ground,
  from how far away can he kick a field goal?

3 m
D
Y-direction vy0 v sin(30) 15 m/s y y0
vyt ½ a t2 3m 0m 15m/s t ½ (9.8 m/s2)
t2 t 2.8 s or t 0.22 s.
x-direction vx0 v cos(30) 26 m/s D x0 vx0
t ½ a t2 0m (26m/s)(2.8 s) 0 m/s2 (2.8
s )2 72.8 m
Illini Kicks 70 yard Field Goal
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