1. Two-Dimensional Motion and VectorsSection 1 Preview Section 1 Introduction to VectorsIntroduction to Vectors Section 2 Vector OperationsVector Operations Section 3 Projectile MotionProjectile Motion Section 4 Relative MotionRelative Motion

2. Two-Dimensional Motion and VectorsSection 1 What do you think? How are measurements such as mass and volume different from measurements such as velocity and acceleration? How can you add two velocities that are in different directions?

3. Two-Dimensional Motion and VectorsSection 1 Introduction to Vectors Scalar - a quantity that has magnitude but no direction –Examples: volume, mass, temperature, speed Vector - a quantity that has both magnitude and direction –Examples: acceleration, velocity, displacement, force

4. Two-Dimensional Motion and VectorsSection 1 Vector Properties Vectors are generally drawn as arrows. –Length represents the magnitude –Arrow shows the direction Resultant - the sum of two or more vectors

5. Two-Dimensional Motion and VectorsSection 1 Vector or Scalar? Acceleration of a planes take off The number of passengers on the plane The duration of a flight The displacement of the flight The amount of fuel required for the flight

6. Two-Dimensional Motion and VectorsSection 1 Finding the Resultant Graphically Method –Draw each vector in the proper direction. –Establish a scale (i.e. 1 cm = 2 m) and draw the vector the appropriate length. –Draw the resultant from the tip of the first vector to the tail of the last vector. –Measure the resultant. The resultant for the addition of a + b is shown to the left as c.

7. Two-Dimensional Motion and VectorsSection 1 Vector Addition Vectors can be moved parallel to themselves without changing the resultant. –the red arrow represents the resultant of the two vectors

8. Two-Dimensional Motion and VectorsSection 1 Vector Addition Vectors can be added –The resultant (d) is the same in each case Subtraction is simply the addition of the opposite vector.

9. Two-Dimensional Motion and VectorsSection 1 Click below to watch the Visual Concept. Visual Concept Properties of Vectors

10. Two-Dimensional Motion and VectorsSection 1 Sample Resultant Calculation A toy car moves with a velocity of.80 m/s across a moving walkway that travels at 1.5 m/s. Find the resultant speed of the car.

11. Two-Dimensional Motion and VectorsSection 1 Practice Problems A roller coaster moves 85 m, then travels 45 m at an angle of 30.0° above the horizontal. What is its displacement from its starting point ? Use the graphical method. –126 m at 10°

12. Two-Dimensional Motion and VectorsSection 1 Practice Problems A novice pilots sets a plane’s controls, thinking the plane will fly at 250 km/h to the north. If the wind blows at 75 km/h toward the south-east, what is the plane’s resultant velocity? Use the graphical method. –58.33 m/s at 75 ° north of east

13. Two-Dimensional Motion and VectorsSection 1 Practice Problems While flying of the Grand Canyon, the pilot slows the plane’s engines down to ½ the velocity in the problem prior. If the wind’s velocity is still 75.km/h toward the south east, what will the plane’s new resultant velocity be? Use the graphical method. –23.61 m/s at 52 ° north of east