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

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Presentation transcript:

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

Photo by Vickie Kelly, 2006 Everglades National Park, FL

Photo by Vickie Kelly, 2006 Everglades National Park, FL

Photo by Vickie Kelly, 2006 Everglades National Park, FL

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.

We can describe the position of a moving particle by a vector, r ( t ). 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.

In three dimensions the component form becomes:

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

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

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.

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

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

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

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

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