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10.2 day 2 Vector Valued Functions

10.2 day 2 Vector Valued Functions. Photo by Vickie Kelly, 2006. Greg Kelly, Hanford High School, Richland, Washington. Everglades National Park, FL. Photo by Vickie Kelly, 2006. Everglades National Park, FL. Photo by Vickie Kelly, 2006. Everglades National Park, FL.

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10.2 day 2 Vector Valued Functions

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  1. 10.2 day 2 Vector Valued Functions Photo by Vickie Kelly, 2006 Greg Kelly, Hanford High School, Richland, Washington Everglades National Park, FL

  2. Photo by Vickie Kelly, 2006 Everglades National Park, FL

  3. Photo by Vickie Kelly, 2006 Everglades National Park, FL

  4. Photo by Vickie Kelly, 2006 Everglades National Park, FL

  5. Any vector can be written as a linear combination of two standard unit vectors. The vector v is a linear combination of the vectors i and j. The scalar a is the horizontal component of v and the scalar b is the vertical component of v.

  6. If we separate r(t) into horizontal and vertical components, we can express r(t) as a linear combination of standard unit vectors i and j. We can describe the position of a moving particle by a vector, r(t).

  7. In three dimensions the component form becomes:

  8. ENTER ENTER GRAPH Y= WINDOW Graph on the TI-89 using the parametric mode. MODE Graph……. 2

  9. ENTER ENTER GRAPH Y= WINDOW Graph on the TI-89 using the parametric mode. MODE Graph……. 2

  10. Most of the rules for the calculus of vectors are the same as we have used, except: “Absolute value” means “distance from the origin” so we must use the Pythagorean theorem.

  11. b) Find the velocity, acceleration, speed and direction of motion at . Example 5: a) Find the velocity and acceleration vectors.

  12. b) Find the velocity, acceleration, speed and direction of motion at . Example 5: velocity: acceleration:

  13. b) Find the velocity, acceleration, speed and direction of motion at . Example 5: speed: direction:

  14. a) Write the equation of the tangent where . At : Example 6: slope: position: tangent:

  15. b) Find the coordinates of each point on the path where the horizontal component of the velocity is 0. The horizontal component of the velocity is . Example 6: p

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