1. Review Components Do Now: Draw a vector that is 40 m/s at 40° North of West  What is the x component of the velocity and the y component of the velocity?  Solve both graphically (with an appropriate scale) and by using trig

2. Quick Experiment ► If two forces act on an object, how can the forces be arranged to get the maximum force? The minimum force? A force in between the maximum and the minimum?  Work with your partner. Choose an object on your desk. Each partner applies a force with your force producer (finger). Figure answer.

3. Resultant ► A single vector that represents the same affect as the addition of 2 or more vectors ► Represented as a dashed line

4. Two Vectors in the Same Direction Mathematically ► 0° angle between them ► Add the magnitudes of the vectors together ► The resultant is the maximum value possible

5. Aim: How can we add two vectors together acting on a point? A girl walks 200 m East and then walks another 400 m East. Draw a scaled representation. Scale: 1 cm = 100 m Resultant = 600 m

6. Two Vectors in Opposite Directions Mathematically ► 180° angle between the vectors ► Subtract the magnitude of the two vectors ► The direction of the resultant is the same as the direction of the larger vector ► The resultant is the minimum value possible

7. A boy runs 50 m West and then runs 20 m East. What distance did the boy run? 70 m What is the boy’s resultant displacement? Scale: 1 cm = 10 m Resultant = 30 m

8. Range of Possible Values ► When two vectors are added together, the resultant can be between the maximum value (when the angle is 0°) and the minimum value (when the angle is 180°) ► Example: Is 9 N a possible value when the forces of 30 N and 20 N act concurrently on an object?  No: the range of values is 50 N maximum and 10 N minimum. 9 N falls outside of that range.

9. A 5 N force directed North and a 3 N force directed East act concurrently (acts on the same point at the same time) Draw the two vectors (Hint: start with a set of axes) Scale: 1 cm = 1 N N S W E

10. ► Make a parallelogram ► The resultant is constructed from the origin of the two vectors to the opposite corner ► Measure the magnitude with the ruler and the angle with the protractor 5.7 cm = 5.7 N 59° North of East N S W

11. Adding Two Vectors at Right Angles Mathematically ► Magnitude is obtained through the Pythagorean Theorem a 2 + b 2 = R 2 (3 N) 2 + (5 N) 2 = R 2 9 N 2 + 25 N 2 = R 2 34 N 2 = R 2 R = 5.8 N N S W 5 N 3 N

12. ► The angle is obtained through SOHCAHTOA N S W 5 N 3 N θ North of East

13. Solve the following problems mathematically and graphically using an appropriate scale A moterboat can move with a velocity of 4 m/s. What is the resultant velocity if:  The boat is traveling with a current of 2.5 m/s south?  The boat is traveling against a current of 2.5 m/s south?  The boat is trying to move perpendicularly (west) across a stream that is flowing south with a current of 2.5 m/s?