Todays Subjets:

a)Understanding the dynamic comparison set

b)Analyse of relative motionusing dynamic comparison set

RELATIVE MOTION

Activities:• Applications• Relative displacement,velocityand acceleration• Vectorial and graphical solutions• Examples

What should be the velocity of the velocity of the jets while landing and lifting off ?

If the velocity of the ship is 50km/h and lift off velocity of the jet is 200km/h (reference from any object on the water) can we find the velocity of the jet with respect to ship ?

Can we calculate the same thing for jet B ?

Is there an effect of wind to these relative motions ?

Relative Displacement

The positions of A and B fromThe center of x,y,z coordinate axis :(Position Vectors)

The position vector of B with respectto A : (relative displacement)

Relative Velocity

Relative velocity of B with respect to A is the derivative of the relative displacement.

or

are the velocities of A and B

is the relative motion of B with respect to A

By the same way :

Relative Acceleration

To find the relative acceleration we take thederivatie of velocity.

or

Solution of the Problems:

-The equations of relative motion are vectorial.- There are two ways to solve these problems.

Equation of velocity can be written at cartesian (x,y,z) coordinates and velocity values can be written as scalar for every direction.Then resultant velocity can be calculated.

Or; by drawing the velocity vectors, with the help of trigonometry we canTake the resultants.Sin and Cos theorems can be used in the solutions

Reminder : Sin,Cos Theorems

For addition and substitution, vectors are written intriangular form.Then; using sin and cos theorems, wefind length and angle of the third side of the triangle. This provides us to calculate the relative velocity and relative acceleration.

Given :

Unknown :

Vectorial method : Write Va and Vb vectors in rectengular coordinates and calculate Va - Vb

Graphical method : Draw the vectors Va and Vb from the center Point.Find VB/A using sin,cos theorem.

Vectorial Method:

km/h

km/h

km/h

km/h

Graphical Method :

We will find :

Cosinus Theorem :

Sinus Theorem :

km/h

km/h

km/h