Welcome back to Physics 211
The room is very full – please move toward
the center and help others find a seat.
Get to know the people next
to you, and work with them
on the clicker questions
during class. You will enjoy
yourself and learn more.
If you need to work on your laptop
during the lecture, please sit at the
back of the room so you don’t
distract other students.
Your Comments
The Three ships V1 and V2 question confuses me. Aren't there too many different
variables that we need to know in order to really answer the question?
I love conceptual physics :)
I would like to discuss more about the vector stuff.
I found the distance a soccer ball is kicked the most difficult. Once sine and cosine
are thrown in, I get a little more confused.
The subtraction of vectors please.
Can we go over these checkpoint problems in class?
Please go over both of the three ships questions.
How much Calculus are we going to be using in this class
It took me a little bit to understand how the vectors worked, but now I think I have
the hang of it. Some further explanation would help.
The ship problem; too many unknowns!
The lectures were great, actually! I understood it.
Vector addition/subtraction when graphed on coordinates.
Lets do a quick recap of calculus
concepts from last lecture…
“Differentiating” is just finding the “Slope”
x(t)
evaluated at t1
In other words, v(t1) tells us
how x(t) is changing at time t1.
t1
t
28
“Integrating” is just finding the “Area”
v(t)
v0
ti
t
tf
How does this tell you distance? This is easy to see if you
start by considering the case of constant velocity v0.
In this case the integral is easy to evaluate:
v(t)
v0
= velocity x time
ti
tf
t
42
Physics 211
Lecture 2
Today's Concepts:
a) Vectors
b) Projectile motion
c) Reference frames
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
Vectors

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
Vector Addition
Clicker Question
 
Vectors A
and B
are shown to the right.
Which of the following best describes A
+B
A
B
C
D
E

A

B
Clicker Question
 
Vectors A
and B
are shown to the right.
Which of the following best describes A
-B
A
B
C
D
E

A

B
Another way to think of subtraction
 
Vectors A
and B
are shown to the right.
Which of the following best describes A
-B

A

B
1) Put vectors tail to tail



2) A
–B
is the vector pointing from the head of B
to the head of A
Vectors in 3D
A vector can be defined in 2 or 3 (or even more) dimensions:
Kinematics in 3D
Three directions are independent but share time
Projectile Motion
Horizontal
Vertical
Boring
Checkpoint
A physics demo launches one marble horizontally while at the same
instant dropping a second marble straight down. Which one hits the
ground first?
A) The launched marble hits first.
B) The dropped marble hits first.
C) They both hit at the same time.
Two balls have the same y0-velocity and
same vertical acceleration. Therefore,
they reach the ground at the same time
DEMO
Train Demo
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
correct
B) At the center of the car
C) Backward of the center of the car
vtrain car
Ball and car start with same x position and x velocity,
Since ax = 0 they always have same x position.
Demo - train
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
Shooting the Monkey…
Dart
x = vo t
1
y = - gt 2
2
Monkey
x = xo
1
y = - gt 2
2
Shooting the Monkey…
Still works even if you shoot upwards!
x = vox t
y = voy t - 1/2 g t 2
y = yo - 1/2 g t 2
Dart hits the
monkey
vtrain car
Projectile Motion & Frames of Reference
Time spent in air depends on vertical motion!
The Ship Problems
“I always have trouble solving purely conceptual
problems/problems without numbers.”
Mechanics Lecture 2,
Checkpoint
A destroyer simultaneously fires two shells with the same initial speed at
two different enemy ships. The shells follow the trajectories shown.
Which ship gets hit first.
Destroyer
Enemy 1
A) Enemy 1
B) Enemy 2
C) They are both hit at the same time
Enemy 2
60% of you got this one right…lets try again
Checkpoint
…Which enemy ship gets hit first?
A) Enemy 1 B) Enemy 2 C) Same
Destroyer
Enemy 1
A) Enemy 1 is closer
B) The height for 2 is lower than 1
C) Both shells were fired with the same initial velocity
Enemy 2
Checkpoint
A destroyer fires two shells with different initial speeds at two different
enemy ships. The shells follow the trajectories shown. Which enemy ship
gets hit first?
Destroyer
Enemy 1
A) Enemy 1
B) Enemy 2
C) They are both hit at the same time
Enemy 2
70% of you got this one right…lets try again
Checkpoint
…Which enemy ship gets hit first?
A) Enemy 1 B) Enemy 2 C) Same
Destroyer
Enemy 1
Enemy 2
A) The distance traveled to ship one is less.
B) It has a greater horizontal component meaning it will be hit first.
C) Since both shells reach the same height, their time in the air must be the
same as well.
Field Goal Example
A 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?
y
x
3m
D
y-direction
voy = vo sin(30o) = 15 m/s
y = yo + voyt + ½ at 2
x-direction
vox = vo cos(30o) = 26 m/s
D = xo + vox t + ½ at 2
3 m = 0 m + (15 m/s) t – ½ (9.8 m/s2) t 2
= 0 m + (26 m/s)(2.8 s) + 0 m/s2 (2.8 s )2
t = 2.8 s or t = 0.22 s.
= 72.8 m