RELATIVE MOTION

What is Relative Motion

Strictly speaking…all motion is relative to something.Usually that something is a reference point that is

assumed to be at rest (i.e. the earth).Motion can be relative to anything…even another

moving object.Relative motion problems involve solving problems

with multiple moving objects which may or may not have motion relative to the same reference point. In fact, you may be given motion information relative to each other.

Relative Velocity:Equations written to relate motion to a frame of reference.

Motion that depends on velocity of an observer.

Motion relative to a frame of reference.

Notation for Relative Motion

We use a combination of subscripts to indicate what the quantity represents and what it is relative to.

For example, “va/b” would indicate

the velocity of “object a” with respect

to “object b”. Object b in this

example is the reference point.

Note: The “reference

point” object is

assumed to be at rest.

What is this guy’s velocity?

He travels 4 meters in 2 seconds going east.

Use Compass on watch to find east.

What is this guy’s velocity?

1 Compared to the ground?

2 What velocity does the earth spin at?

3 What velocity do we revolve around the sun?

Section 3.3

What is this guys velocity?

So what is his frame of reference?

What about now?

What about now?

Frame of referenceA coordinate system from which all measurements are made.

Definition – a coordinate system within which objects, positions, and velocities are measured.

MUST PICK AN ORIGIN before you find speed and velocity.

Frame of reference

If two frames of reference are moving with constant velocity relative to each other, the objects appear to move with their own velocity and the frame’s velocity added together (remember that velocities are vectors).

1 –D Relative motionIf car A is moving 5m/s East and car B, is moving 2 m/s West, what is car A’s speed relative to car B.

So, we want to know…if we are sitting in car B, how fast does car A

seem to be approaching us? Common sense tells us that Car A is

coming at us at a rate of 7 m/s.

How do we reconcile that with the formulas?

2 m/s5 m/s

Car A Car B

1- D and the vector addition formula

Va/e =5 m/s

Car A Car B

Vb/e = -2 m/s

Let’s start with defining the reference frame for the values given. Both cars

have speeds given with respect to the earth.

If we set up the formula using the subscript alignment to tell us what to add,

we get…

Eastsmv

vvv

ba

ebeaba

,/725/

///

We are looking for the velocity of A with respect to B, so va/b = ?

Then we need to solve for va/b .ebbaea vvv ///

So…

Adding velocites.

Remember – Velocities are vectors.

Question – a “wing walker” is walking across the wings of an airplane.

The airplanes velocity

is 20 m/s North.

His velocity is 4 m/s East.

What is his apparent

Velocity to someone on the

ground?

•An airplane drops a care package. Describe the path taken by the care package as seen from the airplane’s frame of reference.

•What about from the ground’s frame of reference?

•If the airplane is speeding up with a constant acceleration, what would the package seem to do?

Falling Care Package

The airplane is moving horizontally with a constant velocity of

+115 m/s at an altitude of 1050m.

Describe the motion of the package from the ground’s frame

Of reference.

Falling Care Package

Describe the motion of the package from the airplanes frame

Of reference.

Example Problem

A plane flies due north with an airspeed of 50 m/s, while

the wind is blowing 15 m/s due East. What is the speed

and direction of the plane with respect to the earth?

What do we know?

apv /

“Airspeed” means the speed of the

plane with respect to the air.

“wind blowing” refers to speed of

the air with respect to the earth. eav /

What are we looking for? “speed” of the plane with respect

to the earth.epv /

We know that the speed and heading of the plane

will be affected by both it’s airspeed and the wind

velocity, so… just add the vectors.eaapep vvv ///

Example Problem (cont.)eaapep vvv ///

So, we are adding these vectors…what does it look like?

Draw a diagram,of the vectors tip to tail! Solve it!

smv ap /50/

N

smv ea /15/

epv /

θ

This one is fairly

simple to solve

once it is set

up…but, that can

be the tricky part.

Let’s look at how

the vector

equation is put

together and how

it leads us to this

drawing.

How to write the vector addition formula

eaapep vvv ///

first last

middlesame

Note: We can use the subscripts to properly line up the

equation. We can then rearrange that equation to solve for any

of the vectors. Always draw the vector diagram, then you can

solve for any of the vector quantities that might be missing

using components or even the law of sines.

Crossing a River

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 relativeto 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?

(c) How far downstream does theboat come to ground?

WSBWBS vvv

What do these subscripts means?

BS = Boat relative to Shore

BW = Boat relative to Water

WS = Water relative to Shore

sm5.4

sm0.2sm0.42222

WSBWBS vvv

WSBWBS vvv

θ = Cos-1 ( X / H)

Cos-1 (2 / 4.5) = 63o

s 450sm4.0

m 1800t

θ = Cos-1 ( X / H)

Cos-1 (2 / 4.5) = 63o

1800 Tan (90-63) =

1800 Tan (27) =

900m.

Also,

450s x 2 m/s = 900m

s 450t

Additional problems:

• A canoe has a velocity of .6 m/s relative to still water. A river has a current of .5 m/s.

• Two docks are 1500 m apart on this river. How long will it take this canoe to make the round trip? (2 docks are on the same side of the river. Go down stream and then back upstream.)

• How long would it have taken a person walking on land at .6 m/s?

Last comments on relative motion

I’m walking. What is the correct frame of reference?

Ground, center of earth, center of sun?

How do I test to find out?

Last comments on relative motion

There is no experiment you can perform to determine (there is no way to tell) what frame of reference you are in.

So, there is no “correct” frame of reference. All are equally valid.

However, we usually pick the one that makes the math easiest to work.

Displacement is relative too!Other quantities can be solved for in this way, including displacement.Remember that d=vt and so it is possible to see a problem that may give you some displacement information and other velocity information but not enough of either to answer the question directlyWhen solving these, be very careful that all the quantities on your diagram and in your vector formula are alike (i.e. all velocity or all displacement). Do not mix them!