Vectors & Two-Dimensional Motion

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Presentation transcript:

Vectors & Two-Dimensional Motion

Vectors in 2D Vectors are a visual representation of motion Vectors of 2D motion are added in order to find the RESULTANT vector In order to add vectors, we use trigonometry

Adding & Drawing Vector Diagrams Vectors are always drawn from tail to tip Vectors can only touch tail to tip

Adding & Drawing Vector Diagrams A man runs 300m east and 400m south. Draw a vector diagram.

Adding Vectors Sam throws a ball north to James and James throws the ball west to Nathan. What is the displacement of the ball?

Use Pythagorean’s Theorem When adding perpendicular vectors, use Pythagorean’s Theorem. A man runs 300m east and 400m south. Draw a vector diagram and find the displacement of the man.

Direction Direction is measured two ways… RECTANGULAR CORDINATE SYSTEM:

ANGLES ARE ALWAYS WRITTEN OPPOSITE OF ADJACENT!!! Direction COMMON CARDINAL SYSTEM: ANGLES ARE ALWAYS WRITTEN OPPOSITE OF ADJACENT!!!

Trigonometry & Direction To solve for direction, trigonometry is used.

Sample Problem (19m @ 28° S of E OR 19m @ 62° E of S) Find the displacement of 6.0m east and 3.2m south. (19m @ 28° S of E OR 19m @ 62° E of S)

Sample Problem (1.3x10²m/s @ 47° N of W OR 1.3x10²m/s @ 43° W of N) Find the velocity of a plane that flies 90m/s west and then 97m/s north. (1.3x10²m/s @ 47° N of W OR 1.3x10²m/s @ 43° W of N)

Homework p. 38 #1 (a-h)