4.2

 In the last section, we dealt with two vectors in the same direction, opposite directions, and at right angles to each other.  In this section we will deal with one vector, and try to figure out the other two sides of the triangle.

 1. draw a coordinate system (a graph)  2. choose the correct formula  3. plug in your numbers (calculator must be in degree mode!)  4. check to see if your answer needs a negative sign (what quadrant is your vector in?)

 For the X side use Ax = Acos θ  For the Y side use Ay = Asin θ

 Draw a vector of a car that travels 60 km to the northwest

 Draw a vector representing a football being thrown 30 m south of east at a 60° angle (that’s physics speak for southeast)

60°

 When you are given a direction to draw your vector, simply follow the directions; north of east, south of east, north of west or south of west.

 If you are only given an angle, start measuring your angle from the positive x axis and move counterclockwise.

 The angle you use in a calculation is always the angle INSIDE the triangle you formed

 Draw a picture showing a golf ball being hit at an angle of 110°  Answer?...

 What are the components of a vector of magnitude 5.6 m at an angle of 47° from the positive x axis?

47°

 Because “solving for the components” means what are the x and y sides of my triangle, I will use Ax = Acos θ for the x side, and Ay = Asin θ for the y side  Here’s how this looks…  Ax = 5.6cos47 ( Ax = 3.82m)  Ay = 5.6sin47 (Ay = 4.09m)

 Since the original vector is in quadrant 1, no.

 P. 74 #’s  P. 79 #’s 25, 26, 27a, 29 (use graph paper or be very careful!) and 30