2.  The line and arrow used in Ch.3 showing magnitude and direction is known as the Graphical Representation ◦ Used when drawing vector diagrams  When using printed materials, it is known as Algebraic Representation ◦ Italicized letter in boldface ◦ d = 50 km SW

3.  Two displacements are equal when the two distances and directions are equal ◦ A and B are equal, even though they don’t begin or end at the same place This property of vectors makes it possible to move vectors graphically for adding or subtracting A

4.  Vectors shown are unequal, even though they start at the same place ◦ C D

5.  The resultant vector is the displacement of the vector additions.  My route to school is  My resultant vector is R  0.50 miles East  2.0 miles North  2.5 miles East  20.0 miles North  2.5 miles East  Resultant Vector = 23 miles NE R

6.  When manipulating graphical reps. of vectors, need a ruler to measure correct length  Take the tail end and place at the head of the arrow ◦ Enroute to a school, someone travels 1.0 km W, 2.0 km S, and then 3.0 km W ◦ Resultant vector =  4.5 km SW

7.  Vectors added at right angels can use the Pythagorean System to find magnitude  If vectors added and angle is something other than 90 o, use the Law of Cosines ◦ R 2 = A 2 + B 2 – 2ABcos θ

8.  Find the magnitude of the sum of a 15 km displacement and a 25 km displacement when the angle between them is 135o. ◦ A = 15 km; B = 25 km; θ = 135 o ; R = unknown ◦ R 2 = A 2 + B 2 – 2ABcos θ ◦ = (25 km) 2 + (15 km) 2 – 2(25km)(15 km)cos135 o ◦ =625 km 2 + 225 km 2 – 750km 2 (-0.707) ◦ =1380 km 2 ◦ R = √1380km 2 ◦ = 37 km

9.  A hiker walks 4.5 km in one direction, then makes a 45 o turn to the right and walks another 6.4 km. What is the magnitude of her displacement?

10.  A person walked 450.0 m North. The person then turned left 65 o and traveled 250.0 meters. Find the resultant vector.

11.  Multiplying a Vector by a scalar number changes its length, but not direction, unless negative ◦ Vector direction is then reversed ◦ To subtract two vectors, reverse direction of the 2 nd vector then add them ◦ Δ v = v 2 – v 1 ◦ Δ v = v 2 + (-v 1 ) ◦ If v 1 is multiplied by -1, the direction of v 1 is reversed and can be added to v 2 to get Δ v

12.  Graphical addition can be used when solving problems that involve relative velocity ◦ School bus traveling at a velocity of 8 m/s. You walk toward the front at 3 m/s. How fast are you moving relative to the street? ◦ v bus relative to street ◦ v you relative to bus ◦ v you relative to the street

13.  When a coordinate system is moving, two velocities add if both moving in the same direction & subtract if the motions are in opposite directions ◦ What if you use the same velocities and walk to the rear of the bus. What is your resultant velocity relative to the street? ◦ v bus relative to the street ◦ v you relative to the bus ◦ v you relative to the street

14.  Suppose an airplane pilot wants to fly from the U.S. to Europe. Does the pilot aim the plane straight to Europe? ◦ No, must take in consideration for wind velocity  v air relative to the ground  v plane relative to air  v plane relative to ground