Relative Motion A red car is driving North at 55 mph (relative to Earth), and a blue car is driving North at 65 mph (relative to Earth). If North is taken as positive, then the velocity of the red car relative to the blue car is ___, and the velocity of the blue car relative to the red car is ___, a)+, -. b)-, +. c)+, +. d)-, -. e)need to know which car is in front.

Using Vector Addition  Step 1: Let v 13 = answer you seek.  Step 2: Identify frames 1 and 3 with person or object.  Step 3: Identify frame 2 -- what’s left?  Step 4: Determine value of v 12 and v 23  If you have v 21 or v 32 : CHANGE THE SIGN when you trade subscripts  Step 5: Plug v 12 and v 23 into eqn to get v 13  Step 6: Check that your answer makes sense!

PAL – CLASSICAL RELATIVITY Form groups of three or four. Your group should consist of three who are represented by subscripts A, B, and C (or you can change them to people’s initials). If you have a fourth person, they can be the recorder, otherwise one of the subscript people should record your data. The three subscript-people will begin together. Person C will stand still; person B will move one distance unit (such as a tile in hallway or stair in lecture hall) every ten seconds; person A will move three distance units every ten seconds — all of this relative to earth. The recorder should record the initial value of each of the following quantities, and then record these quantities again every 10 seconds through 30 seconds. position of A relative to B, x AB 0246 position of B relative to C, x BC 0123 position of A relative to C, x AC 0369 position of B relative to A, x BA position of B relative to B, x BB 0000

PAL – CLASSICAL RELATIVITY RECALL: v=(change in position)/(time interval) Use the data your group recorded to answer these questions: 1)What is the velocity of person A relative to person B? 0.2 units/s 2)What is the velocity of person B relative to person C? 0.1 units/s 3) What is the velocity of person A relative to person C? 0.3 units/s 4)Show that your answers agree with v AC =v AB + v BC 0.3= )What is the velocity of person B relative to person A? -0.2 units/s 6)Show that your answer agrees with the expected pattern v BA =-v AB units/s = -(0.2 units/s ) 7)What is the velocity of person B relative to person B? v BB 0 units/s

PAL – CLASSICAL RELATIVITY Marco and Polo are racing. Marco is in the lead going 100 mph. Polo is going 115 mph. To find how fast Polo is catching up with Marco, answer these questions:  If v 13 = answer, what are 1 and 3? Polo, Marco  What, then, is 2? Earth  What are the values of v 12 and v 32 ? 115 mph & 100 mph  Given that value of v 32, what is v 23 ? -100 mph  Use v 13 = v 12 + v 23 to get your answer. 15 mph  Do the size and sign of answer make sense? yes