1 Relative Motion

8/11/2019 1 Relative Motion

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-Relative Motion-Vector Addition and Subtraction

-Motion in Two Dimensions Intro

PhysicsMrs. Coyle


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Part I Relative Velocity

Vector Addition and Subtraction(Graphical)


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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)


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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


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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?


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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


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Resultant VelocityThe resultant velocity is the net velocity

of an object with respect to a reference

frame.


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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?


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What if you have motion in

two dimensions?


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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)


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Graphical Addition of Vectors Head-to-Tail Method

Parallelogram Method


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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).


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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


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Add vectors A+B using the

head to tail method:

A B

Resultant


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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


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Note

If the drawing is done to scale,measure the resultant.

Convert the value of the resultant usingthe scale of the drawing.


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Add vectors A+B using theparallelogram method:

A

B

B

Resultant


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Add the following vectorsusing the head-to-tail method:

Resultant


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Graphical Vector Subtraction

When subtractingA-B :

Invert vector B to get -B

AddA+(-B) normally


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Subtract vectors A-Bgraphically:

A B

-B

Resultant


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Part II

Constant velocity in each of twodimensions (example: boat & river,

plane and wind)Velocityof Boat inStill WaterVelocity

of River

withrespect tothe

ground


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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)


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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).


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Independence of VectorQuantities

Perpendicular vector quantities areindependent of one another.


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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


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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

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