Name: ___________________________ Period: _______________
Date: __________
AKIBOLA
CHAPTER 3 NOTES
TWO DIMENSIONAL MOTION AND VECTORS
Introduction to vectors
Scalars and Vectors




A scalar quantity ___________________________________________________________________
o Examples are: _______________________________________________________________
A vector quantity ___________________________________________________________________
o Examples are: _______________________________________________________________
Vectors ___________________________________________________________________________
The direction ______________________________________________________________________
The length ________________________________________________________________________
Vectors can be _____________________________________________________________________
Vectors only tell _____________________________________, so a vector ____________________
_____________________________________________________
Vector Operations
Adding Vectors

A resultant is ________________________________________________________
o To add vectors graphically, _________________________________________
o Place the _________________________________________________________
o Vectors ____________________________________________
o To subtract a vector _______________________________________________
 Adding vector example problem:
o A parachutist jumps from a plane. He has not pulled is parachute yet. His weight or force is 800 N
downward. The wind is applying a small drag force of 50 N upward. What is the vector sum of the
forces acting on him?
Answer: _____________

Perpendicular vectors _______________________________________________________________
__________________________________________________________________________ Use the
_________________________________________________________________________________
1
Name: ___________________________ Period: _______________
Date: __________
AKIBOLA
Calculate the magnitude and direction of the resultant in the following vectors:
2.00 m
6.00 m

A vector __________________________________________________________________________
o Multiplying by _______________________________________________________________
___________________________________________________________________________
o Multiplying by _______________________________________________________________
___________________________________
Resolving vectors into components.

Any vector _________________________________________________________________, one that lies
on the _____________________________________________________________________
Force Vectors – Vector resolution practice.

x and y are called the x-vector component and the y-vector component of
r.

The vector components of A are two perpendicular vectors Ax and Ay that
 

are parallel to the x and y axes, and add together vectorally so that A  A x  A y .
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Name: ___________________________ Period: _______________
Date: __________
AKIBOLA
AP PHYSICS – 1: Vectors Worksheet I
1. During a relay race, runner A runs a certain distance due north and then hands off the baton to runner B,
who runs for the same distance in a direction south of east. The two displacement vectors
and
can
be added together to give a resultant vector
. Which drawing correctly shows the resultant vector?
2.
The first drawing shows three displacement vectors,
tail-to-head fashion. The resultant vector is labeled
,
, and
, which are added in a
. Which of the following drawings
shows the correct resultant vector for
3. The first drawing shows the sum of three displacement vectors,
,
, and
. The resultant vector is
labeled
. Which of the following drawings shows the correct resultant vector for
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Name: ___________________________ Period: _______________
Date: __________
AKIBOLA
RELATIVE VELOCITY
 The motion of an object ______________________________________________________________
 These points of view _________________________________________________________________
 Depending on the frame of reference used, _______________________________________________
(Motion of objects is independent of each other)
 Velocity of A relative to B: using the ground as a reference frame
The Language we use:
 VAG : _____________________________________________________________________________
 VBG : _____________________________________________________________________________
 VAB : ____________________________________________________________________________
o _________________________________________
o _________________________________________
o _________________________________________
Example 1:
 The white speed boat has a velocity of 30km/h,N, and the yellow boat a velocity of 25km/h, N, both
with respect to the ground. What is the relative velocity of the white boat with respect to the yellow
boat?
Resultant velocity
 The resultant velocity is ______________________________________________________________
(Motion of objects is dependent on each other)
Example 3:
 An airplane has a velocity of 40 m/s, N, in still air. It is facing a headwind of 5m/s with respect to the
ground. What is the resultant velocity of the airplane?
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Name: ___________________________ Period: _______________
Date: __________
AKIBOLA
Example 4:
 The engine of a boat drives it across a river that is 1800m wide. The velocity of the boat relative to the
water is 4.0m/s directed perpendicular to the current. The velocity of the water relative to the shore
is 2.0m/s.
A. What is the velocity of the boat relative to the shore?
B. How long does it take for the boat to cross the river?
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Name: ___________________________ Period: _______________
Date: __________
AKIBOLA
AP PHYSICS – 1: Relative Velocity Worksheet I
Show all your work for full credit!!
1. At one point during the Tour de France bicycle race, three racers are riding along a straight, level section
of road. The velocity of racer A relative to racer B is VAB; the velocity of A relative to C is VAC; and the
velocity of C relative to B is VCB. If VAB = +6.0 m/s, and VAC = +2.0 m/s, what is VBC ?
2. In a marathon race Chad is out in front, running due north at a speed of
him, running due north at a speed of
. How long does it take for John to pass Chad?
3. A swimmer, capable of swimming at a speed of
speed of
current is
. John is 95 m behind
in still water (i.e., the swimmer can swim with a
relative to the water), starts to swim directly across a 2.8-km-wide river. However, the
, and it carries the swimmer downstream.
A) How long does it take the swimmer to cross the river?
B) How far downstream will the swimmer be upon reaching the other side of the river?
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Name: ___________________________ Period: _______________
Date: __________
AKIBOLA
4. Two friends, Barbara and Neil, are out rollerblading. With respect to the ground, Barbara is skating
due south at a speed of
west at a speed of
. Neil is in front of her. With respect to the ground, Neil is skating due
. Find Neil's velocity (magnitude and direction relative to due west), as seen
by Barbara.
5. Two passenger trains are passing each other on adjacent tracks. Train A is moving east with a speed
of
, and train B is traveling west with a speed of
.
A) What is the velocity (magnitude and direction) of train A as seen by the passengers in
train B?
B) What is the velocity (magnitude and direction) of train B as seen by the passengers in
train A?
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