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Vectors and Scalars

Vectors and Scalars. Physics. Bell Ringer (5 mins) in your notebook. Bell ringer. Bell ringer. Bell ringer. Bell ringer. Objective. We will draw vectors & find the resultant to describe motion in 2-Dimensions

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Vectors and Scalars

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  1. Vectors and Scalars Physics

  2. Bell Ringer (5 mins) in your notebook

  3. Bell ringer

  4. Bell ringer

  5. Bell ringer

  6. Bell ringer

  7. Objective • We will draw vectors & find the resultant to describe motion in 2-Dimensions • I will complete a vector activity to draw vectors & find the resultant using Pythagorean theorem. • 3F “ graphical vector addition” • 4C- analyze motion in 2 dimensions

  8. AGENDA • Review vector vs scalar • Vector notes( write examples) • Pythagorean theorem • Vector map activity • Worksheet

  9. Hannah Bradley- October 13th!!!

  10. Review • Is displacement a vector or scalar? What is the difference between vectors & scalars?

  11. Scalar A SCALAR is ANY quantity in physics that has MAGNITUDE, but NOT a direction associated with it. Magnitude – A numerical value with units.

  12. Vector A VECTOR is ANY quantity in physics that has BOTH MAGNITUDE and DIRECTION.

  13. Learning Check • Is it a vector or scalar quantity? • Temperature • displacement • Time

  14. Cornell Notes • Essential Questions: • What is a vector? • How do we represent vectors? • How do we draw a vector? • What shows the magnitude? • What shows the direction? • When should vectors be added? • When should vectors be subtracted? • What is the resultant vector?

  15. Vectors Vectors Quantities can be represented with; • Arrows • Signs (+ or -) • Angles and Definite Directions (N, S, E, W)

  16. Vectors • One dimensional Vectors can use a “+” or “–” sign to show direction. + 50 m/s a- 45 m b - 9.8 m/s2i+ 60 N h

  17. Vectors • Every Vector has two parts. • A Head and a Tail. Tail Head Vectors are typically illustrated by drawing an ARROW above the symbol. The head of the arrow is used to shows the direction and size of the arrow shows the magnitude.

  18. Applications of Vectors VECTOR ADDITION – If 2 similar vectors point in the SAME direction, add them. • Example: A man walks 54.5 meters east, then another 30 meters east. Calculate his displacement relative to where he started? + 54.5 m, E 30 m, E Notice that the SIZE of the arrow conveys MAGNITUDE and the way it was drawn conveys DIRECTION. 84.5 m, E

  19. Applications of Vectors VECTOR SUBTRACTION - If 2 vectors are going in opposite directions, you SUBTRACT. • Example: A man walks 54.5 meters east, then 30 meters west. Calculate his displacement relative to where he started? 54.5 m, E - 30 m, W 24.5 m, E

  20. Resultant • The resultant vector is the vector representing the sum of two or more vectors.

  21. Finding Resultant • We can use Pythagorean theorem to find the resultant vector of a right handed triangle when given 2 sides.

  22. Finding the Resultant vectors When 2 vectors are perpendicular, you must use the Pythagorean theorem. A man walks 95 km, East then 55 km, north. Calculate his RESULTANT DISPLACEMENT. Finish The hypotenuse in Physics is called the RESULTANT. 55 km, N Vertical Component Horizontal Component Start 95 km,E The LEGS of the triangle are called the COMPONENTS

  23. Vector Treasure Hunt • Create directions that lead to a specific object. • Generate a vector scale map

  24. Objective • We will use a treasure hunt activity to create a vector addition map • I will map the course taken and add vectors & use Pythagorean theorem to find the resultant. • 3F “ graphical vector addition”

  25. Teacher Model • Directions to calculators at the back.

  26. Directions ( 30 minutes) • Groups of 4 • 1 minute to find the object • 10 minutes back track steps and create directions on index cards • Shuffle cards • Group tries to locate object from directions • 10 mins draw map to scale • Add all horizontal vectors( directions) • Add all vertical vectors • Make a right handed triangle where your vertical & horizontal meet.

  27. Create a Map • Map drawn to scale.

  28. Right triangle & solve for R • Fins the Sum of all the vertical parts (N & S) • Find the Sum of the horizontal parts( E & W) • Sum i.e. Add / Subtract

  29. Vector Addition Worksheet • Directions: Read the notes/ examples on the front. • Essential Questions: • What is the main rule for putting two vectors together? • How do you know which side is c2? • Draw the vectors & solve the problems on the back of the work sheet

  30. END

  31. Makiah &Christiana- October 17th!!!

  32. Callie Handy’s October 19th!!!

  33. BUT……what about the direction? since it is a VECTOR we should include a DIRECTION on our final answer. N W of N E of N N of E N of W E W N of E S of W S of E NOTE: When drawing a right triangle that conveys some type of motion, you MUST draw your components HEAD TO TOE. W of S E of S S

  34. BUT…..what about the VALUE of the angle??? Just putting North of East on the answer is NOT specific enough for the direction. We MUST find the VALUE of the angle. To find the value of the angle we use a Trig function called TANGENT. 109.8 km 55 km, N q N of E 95 km,E • Identify the sides given. • Choose the right trig function. • Use inverse & Solve for missing angle. So the COMPLETE final answer is : 109.8 km, 30 degrees North of East

  35. BUT…..what about the VALUE of the angle??? Just putting North of East on the answer is NOT specific enough for the direction. We MUST find the VALUE of the angle. To find the value of the angle we use a Trig function called TANGENT. 109.8 km 55 km, N q N of E 95 km,E So the COMPLETE final answer is : 109.8 km, 30 degrees North of East

  36. What if you are missing a component? Suppose a person walked 65 m, 25 degrees East of North. What were his horizontal and vertical components? The goal: ALWAYS MAKE A RIGHT TRIANGLE! To solve for components, we often use the trig functions since and cosine. H.C. = ? V.C = ? 25 65 m

  37. Example A bear, searching for food wanders 35 meters east then 20 meters north. Frustrated, he wanders another 12 meters west then 6 meters south. Calculate the bear's displacement. 23 m, E - = 12 m, W - = 14 m, N 6 m, S 20 m, N 14 m, N 35 m, E R q 23 m, E The Final Answer: 26.93 m, 31.3 degrees NORTH or EAST

  38. Example A boat moves with a velocity of 15 m/s, N in a river which flows with a velocity of 8.0 m/s, west. Calculate the boat's resultant velocity with respect to due north. 8.0 m/s, W 15 m/s, N Rv q The Final Answer : 17 m/s, @ 28.1 degrees West of North

  39. Example A plane moves with a velocity of 63.5 m/s at 32 degrees South of East. Calculate the plane's horizontal and vertical velocity components. H.C. =? 32 V.C. = ? 63.5 m/s

  40. Example A storm system moves 5000 km due east, then shifts course at 40 degrees North of East for 1500 km. Calculate the storm's resultant displacement. 1500 km V.C. 40 5000 km, E H.C. 5000 km + 1149.1 km = 6149.1 km R 964.2 km q The Final Answer: 6224.14 km @ 8.91 degrees, North of East 6149.1 km

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