Resolving Vectors Chapter 4

Vectors in the same plane, same direction? 5 m 4 m

9 m

Vectors in same plane, opposite direction? 7 m 5 m

2 m

Example 1  Jim Jimson is riding the DART train. The train is traveling at 4 m/s past the station. As the train passes the station, Jim gets up and walks towards the rear (heh, heh) of the car at 1 m/s. How fast does Jim appear to be moving relative to an observer outside the train?

Answer…

3 ms/ in the forward direction!

Vectors at right angles to each other?  Use R 2 = A 2 + B 2 =  A and B are…  R stands for resultant (the combination of A and B)

Example 2  A car is driven 125 km due west, then 65 km due south. What is the magnitude of it’s displacement?

What the...???  Start by drawing a picture!

Answer…

125 km 65 km

 Since these vectors are at right angles, we can use Pythagorean’s Theorem to solve for this one…

 R 2 =  R 2 = 19,850 (we don’t want R 2, we want R)  R = km

Graphically adding vectors?  Keep these things in mind:  Vectors are always added head to tail  Add the vectors in the specified order  Keep you vectors sized appropriately

Example 3  Graphically add the following vectors: A to B to D 5 m A D 6 m B7m C 5 m

Answer…

7m 6 m

Have Fun!