Displacement in Two Dimensions The Cosine and Sine Laws to Determine Vectors

Displacement Vectors When describing motion in two dimensions, the displacement direction must be noted In the diagram below, the 15 m vector can be described as 15 m [W 35° N] –Point west, then turn 35° towards north

The Scale Diagram Method Looking at the diagram below, the displacement of the resultant vector, d T, is the sum of the vectors d 1 and d 2 –d T is the displacement –d 1 and d 2 would be the distance If you use this method, you must remember to convert your final answer back into your proper units

The Cosine and Sine Laws Method Using the sine and cosine laws can allow you to calculate the length of the total displacement vector and its angle of orientation This only works when adding two vectors at a time It may be important to review your angle theorums

Vector Addition by Scale Suppose you walk to a friend’s house, taking a shortcut across an open field. Your first displacement is 140 m [E 35° N] across the field. Then you walk m [E] along the sidewalk. Determine your total displacement using a scale diagram.

Vector Addition Using the Cosine and Sine Laws

Practice Problems Do all 3 practice problems on page 25 of your textbook.

Perpendicular Components of a Vector Method Another way to add vectors is to separate each vector into perpendicular components The components of a vector are the parts of the vector that lie along either the x or y axis This is the same separation that we do when we calculate projectile motion

Vectors Using Trig A polar bear walks towards Churchill, Manitoba. The polar bear’s displacement is 15.0 km [S 60.0° E]. Determine the components of the displacement.

Do the practice problems on page 26

Adding Vectors Algebraically In order to do this, you need to separate each vector into its horizontal and vertical components Once you have everything into separate components, you can obtain the total displacement in each direction Once you have the total displacement in each direction, you can find the total displacement, d T

Example An airplane flies 250 km [E 25° N], and then flies 2802 km [S 13° W]. Using components, calculate the airplane’s total displacement.

Do the practice problems on page 28

Classwork/Homework Page 29 #’s: 2 – 5, 8, 10