Frame of reference

• Physical Definition- a framework that is used for the observation and mathematical description of physical phenomena

• 2 Simple definitions- • 1. how an object experiences or views the

motion;• 2. object’s point of view

How do…• ….people account for a frame of reference?

Takes into account 2 objects:

1. The observer

2. The object being compared to the observer

Consider this still person on the ground

as the observer frame of reference, he is observing a plane in the sky

• He see’s the plane going 100 km/hr

Man’s Velocity = 0 km/hr

Now…

• Consider him moving in the opposite direction as the plane at a rate of 25 m/s, while observing the plane still.

• Relative to the man, what is the plane’s speed?

Man’s Velocity = 25 km/hr

The speed is…• The absolute value of the difference in their two speeds,

while considering their directions:

• Since we are considering opposite directions, we compare them with + and – signs. Since they are opposites, identify one as + and one as - .

• 25 km/hr – (-100 km/hr) = 125 km/hr

• The relative speed of the plane with respect to the man is 125 km/hr

Now…

• Consider him moving in the same direction as the plane at a rate of 25 m/s, while observing the plane still.

• Relative to the man, what is the plane’s speed?

Man’s Velocity = 25 km/hr

The speed is…

• The absolute value of the difference in their two speeds, while considering their directions:

• Since we are considering opposite directions, we compare them with + and – signs. Since they are opposites, identify one as + and one as - .

• 25 km/hr – (100 km/hr) = - 75 km/hr

• The relative speed of the plane with respect to the man is 75 km/hr

Described with Vectors• More importantly, Vector Addition

Speed/Velocity Vectors

If motion does not fall in a straight line

We use create a vector map, and use the Pythagorean Theorem to solve.

a2 + b2 = c2

Resultant Velocity

The resultant velocity is the net velocityof an object with respect to a referenceframe.

-Relative Motion

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?

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?

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?

Example 3- Airplane and Wind

An airplane has a velocity of 40 m/s E. It is facing a headwind of 5m/s West. What is the resultant velocity of the airplane?