9/9/11 Room Frequency BA Clicker Ques,on Announcements    
Three vectors A, B and C are shown. Which vector is S = A + B − C
•  CAPA assignment #3 is due on tonight at 10 pm. •  Mid-­‐Term Exam 1 is next Tuesday Evening (Sept 13th) from 7:30pm to 9:15pm. Your exam room will be announced in Monday’s lecture. €
•  Bring Student ID (A) (B)
(C)
(E) None of these.
(D)
150 151 Vectors Mid-Term Exam I
•  Covers Giancoli Ch.1 – Ch. 3.4, in-class Clicker Questions &
Lectures 1-8, CAPA Sets 1-3 and your Recitation Assignments
and Lab 1.
•  The exam is closed book and no notes allowed. There will be
20-25 multiple choice questions. Bring a #2 pencil for marking
your answer on the scan sheet.
•  Bring a scientific calculator which you know how to operate;
apps on phones or other wireless devices are not allowed.
•  Bring Student ID
•  The exam will have a formula sheet attached; you can view
this sheet under the Exam Information link on the web page
sidebar.
•  An old exam is posted on CULearn for practice.
•  Vector quantities have magnitude AND direction
→  position, displacement, velocity, acceleration
•  Vector direction defined relative to reference frame
→ by angle relative to some axis
→ by components along each axis (ordered pair notation)
•  Calculating vector magnitude from components: •  Pythagorean Theorem
•  Finding components given magnitude and angle: →  Trigonometry
•  Finding vector angle from components: →  Trigonometry with inverse functions
•  Addition & subtraction of vectors: →  by components (e.g., add/subtract x components)
→  graphically (tip-to-tail method)
→  subtraction is addition of “negative” of vector
152 153 Using Vectors in Kinema[cs in 2 Dimensions Displacement Vector Consider the two “position vectors” that specify the location
of a blue ball at two points in time (t1 and t2) in a chosen (x,y)
Reference Frame:
Displacement has magnitude and direction!

From positions we calculate displacement Δ
R
  
ΔR = R2 − R1
y

R1
t1

R2

R1
How? Use components!


R1 = (r1x , r1y )

R2 = (r2 x , r2 y )
t2€
€
  
ΔR = R2 − R1
y
t1

R2
t2
€
x
x
Useful relation:
154 
 
R1 + ΔR = R2
155 €
1 9/9/11 Room Frequency BA Clicker Ques,on You travel east in an airplane for 100 km. You then turn le] 60 degrees and travel 200 km. Room Frequency BA Clicker Ques,on You travel east in an airplane for 100 km. You then turn le] 60 degrees and travel 200 km. North Sqrt(3)*100=170 200 200 100 About how far north of your star[ng point will you be? 100 About how far east of your star[ng point will you be? A) 100 km B) 170 km C) 200 km D) 265 km E) 370 km A)  100 km B)  170 km
C)  200 km D)  265 km E) 370 km 156 Room Frequency BA Clicker Ques,on You travel east in an airplane for 100 km. You then turn le] 60 degrees and travel 200 km. 157 Room Frequency BA Clicker Ques,on You travel east in an airplane for 100 km. You then turn le] 60 degrees and travel 200 km. 4*1002+3*1002 265 km 173 km Sqrt(7) = 2.65 θ 1 200 km A) 28° 100 km 170 km 200 km 265 km 370 km C) 41° D) 47° E) 53° INV TAN(173/200) = 41 deg   
ΔR = R2 − R1
t1
 €
R2
€
159 Room Frequency BA Clicker Ques,on 
ΔR

Velocity has magnitude and direction!
v (average) =
Δt

R1
B) 37° 158 Velocity Vector y
200 km What will be the angle θ from your star[ng point? About how far from of your star[ng point will you be? A) 
B) 
C) 
D) 
E) 
173 km 1 45 deg An object travels from point O back to point O in 1 hour
along an equilateral triangle in which each side is 10 km as
follows:

A

B
t2
Δt = t 2 − t1
O
x

C
Displacement = 0 ! 
ΔR

v (average) =
Δt
€
Direc[on of velocity is direc[on of displacement 160 


| A | = | B | = | C | = 10 km
What is the magnitude of the
object’s average velocity around
the loop?
A) 0 km/h
B) 10 km/h
C) 20 km/h
D) 30 km/h
E) 40 km/h 161 €
2 9/9/11 Clicker Ques,on The Accelera[on Vector Room Frequency BA Consider the two “velocity vectors” that specify the velocity
of a blue ball at two points in time (t1 and t2) in a chosen (x,y)
Reference Frame:
In 1D:   
y
Δv = v 2 − v1
Δv change in velocity
a=
=


Δt
elapsed time
v1
v2
x
In 2D: 
 Δv change in velocity
a=
=
Δt
elapsed time
In 2D: (1)  Acceleration is a vector.
(2)  Direction of acceleration is determined entirely by the change in
162 velocity.
163 Room Frequency BA Clicker Ques,on t1 t2 164 3