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5 minutes 15 mph North 20 miles East 25 Dollars 15 lbs downward 6 knotts at 15° East of North

5 minutes 15 mph North 20 miles East 25 Dollars 15 lbs downward 6 knotts at 15° East of North 23 cm3. Scalars and Vectors. Scalars and Vectors. Scalars. Vectors. Vector = size AND direction Ex: displacement, velocity, acceleration Cannot use normal arithmetic. Ex:

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5 minutes 15 mph North 20 miles East 25 Dollars 15 lbs downward 6 knotts at 15° East of North

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  1. 5 minutes 15 mph North 20 miles East 25 Dollars 15 lbs downward 6 knotts at 15° East of North 23 cm3

  2. Scalars and Vectors

  3. Scalars and Vectors Scalars Vectors • Vector = size AND direction • Ex: displacement, velocity, acceleration • Cannot use normal arithmetic. • Ex: 3mi + 2mi = 1mi 3mi + 2mi = 5 mi 3mi + 2mi = 3.6mi Scalar = magnitude or quantity (size) Ex: mass, energy, money, distance Normal Number Can add, subtract, multiply, etc normally. Ex: 3mi + 2mi = 5mi!

  4. Notation of Vectors (symbol) Angle of vector from positive x-axis Name of vector Magnitude of Vector

  5. 2.3 45°

  6. Adding Vectors Graphically Remember: Head to tail

  7. Vector Components(first, a triangle review)

  8. If C is a vector, then A and B are the vertical and horizontal components However, we are going to use different notations for B and A…..

  9. However, we are going to use different names for A and B θ What are the equations for Cx and Cy?

  10. θ

  11. Vector Addition • Resultant vector • Not the sum of the magnitudes • Vectors add head-to-tail • x-components add to givex-component of resultant • y-components add to givey-component of resultant

  12. Adding Vectors by Components A B

  13. Adding Vectors by Components B A Transform vectors so they are head-to-tail.

  14. Adding Vectors by Components Bx By B A Ay Ax Draw components of each vector...

  15. Adding Vectors by Components B A By Ay Ax Bx Add components as collinear vectors!

  16. Adding Vectors by Components B A By Ay Ry Ax Bx Rx Draw resultants in each direction...

  17. Adding Vectors by Components B A R Ry q Rx Combine components of answer using the head to tail method...

  18. Adding Vectors by Components Use the Pythagorean Theorem and Right Triangle Trig to solve for R and q…

  19. Challenge: The Strongman...

  20. Adding Vectors…A strategy - Draw the vectors • Solve for the components of the vectors • Add the x components together • Add the y components together • NEVER ADD AN X COMPONENT TO A Y COMPONENT! • Redraw your new vector • Solve for the magnitude of the resultant vector (using Pythagorean Theorem) • Solve for the angle of the resultant vector (using tan)

  21. Some Examples Using the Strategy • A hunter walks west 2.5km and then walks south 1.8km. Find the hunter’s resultant displacement (distance and direction). • A man lost ina maze makes three consecutive dispacements so that at the end of the walk he is right back where he started. The first displacement is 8.00m westward, and the second is 13.0m northward. Find the magnitude and direction of the third displacement. • A rock is thrown with a velocity of 23.5m/s at an angle of 22.5 degrees to the horizontal. Find the horizontal and the vertical velocity components. • A boat is rowed east across a river with a constant speed of 5.0m/s. If the current is 1.5m/s to the south, what direction must the boat row to get straight across? What is the speed that it makes good?

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