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, v a/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 reference A 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 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. 5 m/s 2 m/s Car A 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?
1- D and the vector addition formula Let s start with defining the reference frame for the values given. Both cars have speeds given with respect to the earth. V b/e = -2 m/s Car A V a/e =5 m/s Car B We are looking for the velocity of A with respect to B, so v a/b =? If we set up the formula using the subscript alignment to tell us what to add, we get v a / e v a / b v b / e Then we need to solve for v a/b. So v v a / b a / b v a / e 5 v b / e 2 7m / s, East
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? 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. What are we looking for? speed of the plane with respect to the earth. 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. v p / e v p / v a / a v p / e vp / a va / e e
Example Problem (cont.) v p / e vp / a va / e So, we are adding these vectors what does it look like? Draw a diagram,of the vectors tip to tail! Solve it! N v p / a 50m / v a / e 15m / s θ s v p / e 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 v v v p / e p / a a / e middle same first last 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 relative to 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 the boat come to ground?
v BS v v BW WS What do these subscripts means? BS = Boat relative to Shore BW = Boat relative to Water WS = Water relative to Shore
v BS v v BW WS v BS v 2 BW v 2 WS 2 4.0m s 2.0m s 2 4.5m s θ = Cos -1 ( X / H) Cos -1 (2 / 4.5) = 63 o
t 1800 m 4.0m s 450 s θ = Cos -1 ( X / H) Cos -1 (2 / 4.5) = 63 o 1800 Tan (90-63) = 1800 Tan (27) = 900m. Also, 450s x 2 m/s = 900m
t 450s
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 directly When 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!