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					              Physics 211
               Lecture 2



Today's Concepts:
  a) Vectors
  b) Projectile motion
  c) Reference frames
                         Vectors

                                    A vector A may be shown is bold
                  Ay                face or with an arrow over it. We
                                    will usually use the “arrow notation”;
                                   That is certainly easier in your hand-
                           A        written notes!


                               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




                                                                             5
                         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




                                                               5
                         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




                                                               5
Vector Addition




                  7
                             ACT
                                                 
                                               A
Vectors Aand Bare shown to the right.              
Which of the following best describes A+ B           B




     A         B         C         D         E




                                                         9
                             ACT
                                                 
                                               A
Vectors Aand Bare shown to the right.              
Which of the following best describes A- B           B




     A         B         C         D         E




                                                         11
                             ACT
                                                  
                                                A
Vectors Aand Bare shown to the right.               
Which of the following best describes A+ 2B           B




     A         B         C         D          E




                                                          13
                  Vectors in 3D


A vector can be defined in 2 or 3 (or even more) dimensions:




                                                               14
                  Vectors in 3D


A vector can be defined in 2 or 3 (or even more) dimensions:




                                                               14
                                    Vectors in 3D


               A vector can be defined in 2 or 3 (or even more) dimensions:

Scalar quantities, like the magnitude
of a vector, show up not in bold and
without an arrow. To emphasize this,
we may use absolute value bars,

   A = | A | or A = | A |




                                                                              14
        Kinematics in 3D




Three directions are independent but share time



                                                  15
             Projectile Motion
Horizontal        Vertical       Boring




                                          16
                          Checkpoint 1
A physics demo launches one marble horizontally while at the same
instant dropping a second marble straight down. Which one hits the
ground first?




                                      Both are accelerating downward with the
 A) The launched marble hits first.   same rate regardless of initial x velocity
 B) The dropped marble hits first.                   DEMO
 C) They both hit at the same time.
                                                                                   20
                      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          correct
 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
                                                                           23
                    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




                                                                           26
        Shooting the Monkey…




Dart
                               Monkey
x = vo t
                               x = xo
      1 2
y = - gt                              1 2
      2                        y = - gt
                                      2




                                            27
                    Shooting the Monkey…

Still works even if you shoot upwards!
                                           y = yo - 1/2 g t 2




 y = voy t - 1/2 g t 2                       Dart hits the
                                               monkey



                                                                30
vtrain car
Projectile Motion & Frames of Reference




          Time spent in air depends on vertical motion!


                                                          31
                            Checkpoint 2
 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                                    Enemy 2


 A) Enemy 1                              67% of you got this one right…lets try again
 B) Enemy 2
 C) They are both hit at the same time

                                                                                    34
                                 Checkpoint 2
  …Which enemy ship gets hit first?
  A) Enemy 1 B) Enemy 2 C) Same




Destroyer                           Enemy 1                               Enemy 2
A) The vertical component is the same and therefore you can concentrate on the
horizontal component. Enemy 1 is closer and will get hit first.

B) The shell fired at ship one goes higher in the vertical direction so it will be in
the air longer since the vertical velocity determines the time of flight
C) Since they have the same initial speeds the two shells will hit both ships at
the same time.
                            Checkpoint 3
 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                                    Enemy 2

 A) Enemy 1                              70% of you got this one right…lets try again
 B) Enemy 2
 C) They are both hit at the same time


                                                                                    38
                                   Checkpoint 3
  …Which enemy ship gets hit first?
  A) Enemy 1 B) Enemy 2 C) Same




Destroyer                             Enemy 1                                      Enemy 2

A) Since the initial speed for the first shell is lower, Enemy Ship 1 will be hit first.

B) The initial speed of the shell fired at ship 2 is greater, so ship 2 gets hit first.

C) they both achieve the same height so they remain in the air the same amount of
time
                               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                                                x-direction
voy = vo sin(30o) = 15 m/s                              vox = vo cos(30o) = 26 m/s
 y = yo + voyt + ½ at 2                                 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



                                                                                             50

				
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