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Finding the Area and Vector Directions: Regression Presentation Project

This text provides step-by-step instructions for finding the area and understanding vector directions, along with examples and practice problems.

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Finding the Area and Vector Directions: Regression Presentation Project

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  1. Do now problem: find the area. Step 1: Find the semiperimeter S = (7 + 8 + 10)/2 S = 12.5

  2. Find the area: Step 2: Use Heron’s Formula A = 27.8 in2

  3. Regression Presentation Project • Group 1 – Tom, Lily, and Sammi • Group 2 – Michael, Justin G., and Najla • Group 3 – Lucy, Tu, and Gwyneth • Group 4 – Wen, Aidan, and William • Group 5 – Andrew, Bryn, and Jake • Group 6 – Stephen, Dennis, and Nick • Group 7 – Jules, Virginia, and Sophie • Group 8 – Justin S., Rachel, and Zoe • Group 9 – Brenda, Lynnete, and Amy • Group 10 – Jeffrey and Jenny

  4. Do Now Problem #2: • Gronk ran an out route for another TD. He ran 12 yards forward, then turned exactly 900 to his right and ran 5 yards before catching the pass. If Brady scrambled directly to the line scrimmage before throwing the pass, then how far did the ball travel? Describe what the various distances mean.

  5. Scalars and Vectors Scalar Vector A vector is a quantity that has both:magnitude(size) anddirection • A scalar is a quantity that has magnitude without direction

  6. Vector or not a vector?

  7. Mr. Rice driving 30mph • No, what is the direction? • This is a scalar quantity

  8. Mr. Rice eating 2 veggie hot dogs per minute • No, what is the direction? • This is a scalar quantity

  9. Mr. Rice walking 4mph north down Comm Ave • Yes, this is a vector • This has magnitude and direction

  10. Split these into 2 groups • Scalars • Vectors • Temperature • Mass • Kinetic energy • Time • Amount • Density • Charge • Speed • Velocity • Acceleration • Distance • Displacement

  11. Vectors Two types of quantities exist in the world: • Scalers – a quantity with a value but without direction • i.e. speed = 12 m/s • Vectors – a quantity with magnitude (value) and a direction (heading) • i.e. velocity = 12 m/sdue north • Scalersinclude: • Speed, energy, time, work, distance, mass • Vectors include: • Velocity, acceleration, force, momentum, displacement

  12. Vector Direction • Lets learn about directions for vectors. • We use a compass for basic direction/headings N E W S

  13. N 24 m/s Vector Direction • If a vector is heading along one of the main heading (such as N, E, S, or W) just give it that direction • i.e. A train has a velocity of 24 m/s (S)

  14. Vector Direction • If the vector is exactly mid-way between two main headings then we can use: • 45o N of W or • NW, SW, SE, SW as the direction N NW NE 45o 45o W E SE SW S

  15. 24 m/s 32o E W S Vector Direction • But what about other directions? • In this case we use a direction from one of the main headings (N, E, S, or W) • This vector would become: • 24 m/s at 32o N of E N The vector direction 32o above the main EAST direction. Hence we say 32o N of E.

  16. Vector Direction • There is another way of indicating this direction • In this case we use a direction measured away from the north direction • This vector would become: • 24 m/s at 58o E of N The vector direction 58o from the main North direction. Hence we say 58o E of N. 24 m/s N 58o E W S

  17. Vector Direction • Every vector has two ways of indicating directions • You only need to state one of them • For example: • 65 m at 22o N of W or • 65 mat 68o W of N (same direction) Note: The two directions must always add up to 90o. Why? N 65 m 68o 22o E W Remember, you only need one direction! S

  18. Vector Direction • Now try these: State the magnitude of each vector and give both possible directions 35 N N N 24o 13o 45 m Vector = Vector = 45 m at 13o S of E 35 N at 240 N of W 45 m at 77o E of S 35 N at 66o W of N

  19. But it could be confusing

  20. Vector Direction • Bearing – another direction system used by airplanes and ships for navigation N 0o 90o 270o 180o

  21. Vector Direction • This is easy: • 24 Km bearing 125o(90o + 35o) N 0o 90o 270o 35o 180o 24 Km bearing 125o

  22. Vector Direction 250 km bearing 45o • Now try these: 250 km N 0o 45o 225 km 60o 225 km bearing 270o 180o 210 km 210 km bearing 150o

  23. Lets Try Some Harder Problems

  24. Vectors #1 N Adj 2km You can use vectors to describe displacements A girl walks 2km due east from a fixed point O, to A, and then 3km due south from A to a point B. Describe the displacement of B from O. • Start, as always, with a diagram! • To describe the displacement you need the distance from O as well as the direction (as a bearing) • Remember bearings are always measured from north! “Point B is 3.61km from O on a bearing of 146˚” O A θ 56.3˚ 3km Describing the displacement Opp The distance – use Pythagoras’ Theorem B Sub in a and b Calculate The bearing – use Trigonometry to find angle θ Sub in opp and adj Use inverse Tan Bearings are measured from north. Add the north line and add 90˚ 6A

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