Download - 1 Relative Motion
-
8/11/2019 1 Relative Motion
1/26
-Relative Motion-Vector Addition and Subtraction
-Motion in Two Dimensions Intro
PhysicsMrs. Coyle
-
8/11/2019 1 Relative Motion
2/26
Part I Relative Velocity
Vector Addition and Subtraction(Graphical)
-
8/11/2019 1 Relative Motion
3/26
Relative VelocityVelocity 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)
-
8/11/2019 1 Relative Motion
4/26
Example 1
The white speed boat has a velocity of30km/h,N, and the yellow boat avelocity of 25km/h, N, both with respectto the ground. What is the relative
velocity of the white boat with respectto the yellow boat?
Answer: 5km/h, N
-
8/11/2019 1 Relative Motion
5/26
Example 2-
The 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?
-
8/11/2019 1 Relative Motion
6/26
Example 2 -continuedThe passenger decides to approach thedriver with a velocity of 1 m/s, N, with
respect to the bus, while the bus is movingat 5m/s, N.
What is the velocity of the passenger withrespect to the ground?
Answer: 6m/s, N
-
8/11/2019 1 Relative Motion
7/26
Resultant VelocityThe resultant velocity is the net velocity
of an object with respect to a reference
frame.
-
8/11/2019 1 Relative Motion
8/26
Example 3- Airplane and WindAn 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 theairplane?
-
8/11/2019 1 Relative Motion
9/26
What if you have motion in
two dimensions?
-
8/11/2019 1 Relative Motion
10/26
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)
-
8/11/2019 1 Relative Motion
11/26
Graphical Addition of Vectors Head-to-Tail Method
Parallelogram Method
-
8/11/2019 1 Relative Motion
12/26
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).
-
8/11/2019 1 Relative Motion
13/26
Head-to-Tail Method ofMethod Addition
Move one vector parallel to itself, so thatits 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.
B
Resultant
A
-
8/11/2019 1 Relative Motion
14/26
Add vectors A+B using the
head to tail method:
A B
Resultant
-
8/11/2019 1 Relative Motion
15/26
Place the vectors tail to tail forming a
parallelogram.
Draw the diagonal from the two tails.This is the resultant.
A
B
Resultant
Parallelogram Method ofVector Addition
-
8/11/2019 1 Relative Motion
16/26
Note
If the drawing is done to scale,measure the resultant.
Convert the value of the resultant usingthe scale of the drawing.
-
8/11/2019 1 Relative Motion
17/26
Add vectors A+B using theparallelogram method:
A
B
B
Resultant
-
8/11/2019 1 Relative Motion
18/26
Add the following vectorsusing the head-to-tail method:
Resultant
-
8/11/2019 1 Relative Motion
19/26
Graphical Vector Subtraction
When subtractingA-B :
Invert vector B to get -B
AddA+(-B) normally
-
8/11/2019 1 Relative Motion
20/26
Subtract vectors A-Bgraphically:
A B
-B
Resultant
-
8/11/2019 1 Relative Motion
21/26
Part II
Constant velocity in each of twodimensions (example: boat & river,
plane and wind)Velocityof Boat inStill WaterVelocity
of River
withrespect tothe
ground
-
8/11/2019 1 Relative Motion
22/26
Adding vectors that are at 900to each other.
Draw the vector diagram and draw theresultant.
Use the Pythagorean Theorem tocalculate the resultant.
Use =tan-1(y/x) to find the angle
between the horizontal and theresultant, to give the direction of theresultant. (00 is along the +x axis)
-
8/11/2019 1 Relative Motion
23/26
Example 4-Airplane and Wind
An airplane is traveling with a velocity of 50m/s, E with respect to the wind. The wind is
blowing with a velocity of 10 m/s, S. Findthe resultant velocity of the plane withrespect to the ground.
Answer: 51m/s, at 11obelow the + x axis (E).
-
8/11/2019 1 Relative Motion
24/26
Independence of VectorQuantities
Perpendicular vector quantities areindependent of one another.
-
8/11/2019 1 Relative Motion
25/26
Independence of VectorQuantites Example: The constant velocities in each of
the two dimensions of the boat & riverproblem, are independent of each other.
Velocityof Boat inStill WaterVelocity
of River
withrespect tothe
ground
-
8/11/2019 1 Relative Motion
26/26
Example 5- Boat and River
A boat has a velocity of 4 m/s, E, in stillwater. It is in a river of width 150m, that
has a water velocity of 3 m/s, N.a) What is the resultant velocity of the boat
relative to the shore.
b)
How far downstream did the boat travel?
Answer: a) 5m/s, @ 37oabove + x axis (E)b) 113m