Teacher notes: EQ: How does motion (even constants) Change depending on how you look at it? We will discuss what a frame of reference is, and how it effects what we see. I will be able to identify different frames of reference. Exit slip: describe a situation where free fall acceleraton (a constant) is NOT -9.81m/s 2

EQ: How does the motion of an object change when viewed from different frame of references?

*If you are in an elevator without signs or lights, how do you know if you are going up or down or that you are moving at all? *Why can you not feel yourself spinning if the earth is spinning 1000 mi/hr at the equator? What is moving?

It all depends on how you look at it Frame of reference A coordinate system from which motion us viewed The point of view of an observer The velocity, displacement, and acceleration can all be different for different observers The motion itself is not really different, it’s just viewed different RELATIVE to you

If you are traveling north on I-10 at 60mph, and a cop speeds past you going 90mph, How fast does it look to you in your car? What velocity does the cop see you going?

You have to use your imagination! 90mph 60mph

Looking out your window, you see the cop pass slowly (30mph)

The cop sees you going, slowly backward (30mph)

Adding and Subtracting Vectors When an object moves in a moving frame of reference, you add the velocities if they are in the same direction. You subtract one velocity from the other if they are in opposite directions. You are traveling in a school bus with a velocity of 8 m/s in the positive direction, you walk with a velocity of 1 m/s toward the front of the bus. Your mom is waiting for you and is observing you from the road, what velocity do you appear to be moving from your mom’s frame of reference? bus relative to street 8 m/s You relative to bus 1 m/s You relative to street 9 m/s

1 –D Relative motion If 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

Formu la Velocity of A relative to B: V AB + V BE = V AE (You will be using subscripts to show each one of the points you are comparing) v AB : v of A (object) with respect to B (object) v BE : v of B (object) with respect to a reference frame E (Earth) v AE : v of A (object) with respect to a reference frame E (Earth)

What would happen if… A truck was traveling west (left) at 15mph You are traveling in the truck, and kick a soccer ball east(right) with a velocity relative to you of 15mph Draw Vectors to represent this senerio

1- D and the vector addition formula V a/e =5 m/s Car A Car B V b/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… We are looking for the velocity of A with respect to B, so v a/b = ? Then we need to solve for v a/b. So…

Example 1 The white speed boat has a velocity of 30 km/h, N, and the yellow boat a velocity of 25 km/h, N, both with respect to the ground. What is the relative velocity of the white boat with respect to the yellow boat? G: White boat (A) - 30 km/h, N Yellow boat (B) - 25 km/h, N Ground (E – Earth) U: Velocity of white boat (A) to Yellow boat (B) E: S: 30 = v a/b + 25 v a/b = 5 km/h N

Example 2: You are sitting in an airport watching a plane land v = 100 m/s East. The stewardess is walking down the isle East. To the people in the plane she seems to be walking 2 m/s. Plane: v PE = 100 m/s to Earth Stewardess: v SP = 2 m/s to Plane How fast does the stewardess appear to move to you observer in the airport? v SE = v SP + v PE  2 m/s m/s

Example 3-Football A player is running to tackle the running back. The running back is moving 8 m/s east and the defense is moving 6 m/s right across the field west. What is the velocity of the running back relative to the defense? G: Running Back (R) = 8 m/s Defense (D) = -6 m/s U: Velocity of running back relative to the defense (v RD ) E: S: 8 m/s = V R/D + (-6 m/s) V R/D = 8 m/s - (-6 m/s) S: v RD = 14 m/s

Example 4- 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? 5 m/s North b)with respect to the bus? 0 m/s

Example 4 -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? Answer: 6m/s, N

Practice ! ! ! A bored passenger on a train is throwing a ball straight up and down. Draw and label (velocity & acceleration) this scenario. From his point of view… From the point of view of a stationary observer watching the train 45m/s to the left.

The guy on the train. a = -9.81m/s constant X velocity ( V x ) Is constant at 0m/s The Y velocity (V y ) positive at first, slowing down zero at the top Negative & speeding up

The guy at the train station. a = -9.81m/s constant X velocity ( V x ) Is constant at 45m/s The Y velocity (V y ) positive at first, slowing down zero at the top Negative & speeding up

Lets do some Work ! ! ! Be sure to draw a picture for each situation! Draw and label all vectors