-Relative Motion
-Vector Addition and Subtraction
-Motion in Two Dimensions Intro
Physics
Mrs. Coyle
Part I


Relative Velocity
Vector Addition and Subtraction
(Graphical)
Relative Velocity
Velocity of A relative to B:
VAB=VA-VB
vAB : v of A with respect to B
vB : v of B with respect to a reference
frame (ex.: the ground)
vA : v of A with respect to a
reference frame (ex.: the ground)
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?
Answer: 5km/h, N
Example 2The Bus Ride
A passenger is seated on a bus that is
traveling with a velocity of 5 m/s, North.
If the passenger remains in her seat,
what is her velocity:
a)
with respect to the ground?
b)
with respect to the bus?
Example 2 -continued
The passenger decides to approach the
driver with a velocity of 1 m/s, N, with
respect to the bus, while the bus is moving
at 5m/s, N.
What is the velocity of the passenger with
respect to the ground?
Answer: 6m/s, N
Resultant Velocity
The resultant velocity is the net velocity
of an object with respect to a reference
frame.
Example 3- Airplane and Wind
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?
What if you have motion in
two dimensions?
Motion in Two Dimensions


Constant velocity in each of two
dimensions (example: boat & river,
plane and wind)
Projectiles (constant velocity in one
dimension and constant acceleration in
the other dimension)
Graphical Addition of Vectors

Head-to-Tail Method

Parallelogram Method
Some rules to use for vector
addition:


Vectors can be moved parallel to
themselves. Their magnitude and
direction is still the same.
The order of vector addition does not
effect the resultant (commutative
property).
Head-to-Tail Method of
Method Addition


Move one vector parallel to itself, so that
its head is adjacent to the tail of the other
vector.
Draw the resultant by starting at the first
tail and ending at the last head.
A
B
Resultant
Add vectors A+B using the
head to tail method:
A
Resultant
B
Parallelogram Method of
Vector Addition


Place the vectors tail to tail forming a
parallelogram.
Draw the diagonal from the two tails.
This is the resultant.
A
Resultant
B
Note


If the drawing is done to scale, measure
the resultant.
Convert the value of the resultant using
the scale of the drawing.
Add vectors A+B using the
parallelogram method:
B
A
B
Resultant
Add the following vectors
using the head-to-tail method:
Resultant
Graphical Vector Subtraction
When subtracting A-B :


Invert vector B to get -B
Add A+(-B) normally
Subtract vectors A-B
graphically:
Resultant
A
B
-B
Part II

Constant velocity in each of two
dimensions (example: boat & river,
plane and wind)
Velocity
of River
with
respect to
the
ground
Velocity
of Boat in
Still Water
Adding vectors that are at 900
to each other.



Draw the vector diagram and draw the
resultant.
Use the Pythagorean Theorem to
calculate the resultant.
Use θ=tan-1(y/x) to find the angle
between the horizontal and the
resultant, to give the direction of the
resultant. (00 is along the +x axis)
Example 4-Airplane and Wind
An airplane is traveling with a velocity of 50
m/s, E with respect to the wind. The wind is
blowing with a velocity of 10 m/s, S. Find
the resultant velocity of the plane with
respect to the ground.
Answer: 51m/s, at 11o below the + x axis (E).
Independence of Vector
Quantities

Perpendicular vector quantities are
independent of one another.
Independence of Vector
Quantites

Example: The constant velocities in each of
the two dimensions of the boat & river
problem, are independent of each other.
Velocity
of River
with
respect to
the
ground
Velocity
of Boat in
Still Water
Example 5- Boat and River
a)
b)
A boat has a velocity of 4 m/s, E, in still
water. It is in a river of width 150m, that
has a water velocity of 3 m/s, N.
What is the resultant velocity of the boat
relative to the shore.
How far downstream did the boat travel?
Answer: a) 5m/s, @ 37o above + x axis (E)
b) 113m