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-Relative Motion -Vector Addition and Subtraction -Motion in Two Dimensions Intro

-Relative Motion -Vector Addition and Subtraction -Motion in Two Dimensions Intro. Physics Mrs. Coyle. Part I. Relative Velocity Vector Addition and Subtraction (Graphical). Relative Velocity. Velocity of A relative to B: V AB = V A - V B v AB : v of A with respect to B

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-Relative Motion -Vector Addition and Subtraction -Motion in Two Dimensions Intro

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  1. -Relative Motion-Vector Addition and Subtraction -Motion in Two Dimensions Intro Physics Mrs. Coyle

  2. Part I • Relative Velocity • Vector Addition and Subtraction (Graphical)

  3. Relative Velocity Velocity of A relative to B: VAB=VA-VB vAB : v of A with respect to B vB : v of B with respect to a reference frame (ex.: the ground) vA : v of A with respect to a reference frame (ex.: the ground)

  4. 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? • Answer: 5km/h, N

  5. 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: • with respect to the ground? • with respect to the bus?

  6. 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? Answer: 6m/s, N

  7. Resultant Velocity The resultant velocity is the net velocity of an object with respect to a reference frame.

  8. Example 3- Airplane and Wind An airplane has a velocity of 40 m/s, N, in still air. It is facing a headwind of 5m/s with respect to the ground. What is the resultant velocity of the airplane?

  9. What if you have motion in two dimensions?

  10. Motion in Two Dimensions • Constant velocity in each of two dimensions (example: boat & river, plane and wind) • Projectiles (constant velocity in one dimension and constant acceleration in the other dimension)

  11. Graphical Addition of Vectors • Head-to-Tail Method • Parallelogram Method

  12. Some rules to use for vector addition: • Vectors can be moved parallel to themselves. Their magnitude and direction is still the same. • The order of vector addition does not effect the resultant (commutative property).

  13. Head-to-Tail Method of Method Addition • Move one vector parallel to itself, so that its head is adjacent to the tail of the other vector. • Draw the resultant by starting at the first tail and ending at the last head. B A Resultant

  14. Add vectors A+B using the head to tail method: A B Resultant

  15. Parallelogram Method of Vector Addition • Place the vectors tail to tail forming a parallelogram. • Draw the diagonal from the two tails. This is the resultant. A Resultant B

  16. Note • If the drawing is done to scale, measure the resultant. • Convert the value of the resultant using the scale of the drawing.

  17. Add vectors A+B using the parallelogram method: B A Resultant B

  18. Add the following vectors using the head-to-tail method: Resultant

  19. Graphical Vector Subtraction When subtracting A-B : • Invert vector B to get -B • Add A+(-B) normally

  20. Subtract vectors A-B graphically: Resultant A B -B

  21. Part II • Constant velocity in each of two dimensions (example: boat & river, plane and wind) Velocity of Boat in Still Water Velocity of River with respect to the ground

  22. Adding vectors that are at 900 to each other. • Draw the vector diagram and draw the resultant. • Use the Pythagorean Theorem to calculate the resultant. • Use θ=tan-1(y/x) to find the angle between the horizontal and the resultant, to give the direction of the resultant. (00 is along the +x axis)

  23. Example 4-Airplane and Wind An airplane is traveling with a velocity of 50 m/s, E with respect to the wind. The wind is blowing with a velocity of 10 m/s, S. Find the resultant velocity of the plane with respect to the ground. Answer: 51m/s, at 11o below the + x axis (E).

  24. Independence of Vector Quantities • Perpendicular vector quantities are independent of one another.

  25. Independence of Vector Quantites • Example: The constant velocities in each of the two dimensions of the boat & river problem, are independent of each other. Velocity of Boat in Still Water Velocity of River with respect to the ground

  26. Example 5- Boat and River A boat has a velocity of 4 m/s, E, in still water. It is in a river of width 150m, that has a water velocity of 3 m/s, N. • What is the resultant velocity of the boat relative to the shore. • How far downstream did the boat travel? Answer: a) 5m/s, @ 37o above + x axis (E) b) 113m

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