Objective

1. Objective • We will determine displacement using vector addition with the Pythagorean Theorem and the inverse tangent function.

2. Bell Ringer, 9/24 Draw a diagram of a hiker walking 3km east and then 6km north. We know they covered a distance of 9km. Can you think of a way that we can determine their displacement?

3. Use these slopes for today’s assignment

4. Instructions • 1. Draw the slopes as vectors on graph paper. - in vector form the horizontal direction is denoted with i and the vertical direction is denoted by j. • Ex: 7/4 becomes: 4i + 7j

5. 2. You add the vectors by plotting them on a graph from head to tail – draw the i vector (in our case, 4i) in the positive direction on the x-axis. • - next draw the j vector placing its tail at the head of the i vector. • 3. You can now indicate the resultant vector R, by connecting the head of the j vector with the origin.

6. 4. calculate the length of the resultant using the Pythagorean theorem: a2 + b2 = c2

7. 5. You can find the direction of the resultant vector using the inverse tangent function. • The inverse tangent of the slope = the angle theta. • To do this tap the 2nd key on the calculator and then the tan key. • You will see an open parenthesis – enter the slope, which in our example is 4/7. • The calculator should be in degree mode: tap the mode key, select degrees from the third row down and tap enter.

8. Product • Given an i vector and a j vector, explain how we determine the displacement of the object.