GIG Read the passage and mark your answers on your whiteboard. NOT ON THE PAPER. Questions 3-4.

Adding and Subtracting Vectors

A Treasure Map A treasure map tells you to start at the sycamore tree, walk 5 paces north and 3 paces east. Doing so gets you to the treasure. If you walked directly from the tree to the treasure, would your displacement have changed?

Adding Vectors Vectors can be visually represented with arrows. You can add vectors by placing the tip of one vector to the tail of another. The resultant vector is the displacement (magnitude) and direction (angle) of added vectors.

Adding the Components of the Vectors Works You can break each vector into its x and y components and add them, and end up with the correct x,y coordinate for total displacement.

Subtracting Vectors Sometimes a problem will ask you to subtract a vector. This means changing the sign of the vector’s x and y components (visually, turning the vector 180 degrees). Line up this reversed vector tip to tail with the others.

Sample Problem - Try Solving on Whiteboard Find the magnitude and angle of displacement of a person who walks the following three paths on a flat field. First, he walks 25 m heading 49° north of east. Then, he walks 23 m heading 15° north of east. Finally, he turns and walks 32 m in a direction 68° south of east. Break each vector into its components with trigonometry, then add them.

Sample Problem - Try Solving on Whiteboard First vector - x component 25m(cos(49)) = 16.40m First vector - y component 25m(sin(49)) = 18.87m

Sample Problem - Try Solving on Whiteboard Second vector - x component 23m(cos(15)) = 22.22m Second vector - y component 23m(sin(15)) = 5.953m

Sample Problem - Try Solving on Whiteboard Third vector - x component 32m(cos(68)) = 11.99 m Third vector - y component -32m(sin(68)) = -29.67m

Sample Problem - Try Solving on Whiteboard Add the x and y components x y 16.40m 18.87m 22.22m 5.953m 11.99m -29.67m 50.61m -4.847m

Sample Problem - Try Solving on Whiteboard Use the Pythagorean theorem to find the magnitude of total displacement. 50.61m2 + (-4.8472m)2 = displacement2 = 2584.866m2 √2584.866m2 = 50.84m

Sample Problem - Try Solving on Whiteboard Finally, use the trigonometry to find the angle. One option is tan θ = 4.847 / 50.61 θ = 5.471° S of E ** Enter tan-1(4.847/50.61) ** 50.61m θ 4.847 50.84m

Sample Problem - Try Solving on Whiteboard Put it all together with significant figures Displacement = 51m Angle = 5.5° south of east.

Final Result (Less Accurate Visual Addition Method)

Note that you can add the vectors in any order.

Read pages 121-126 in textbook Discuss LessonCheck questions on page 126 with table partners.

Homework Be prepared for 1-D motion test on block day.

Closure Answer on your whiteboard: You drive 2.4 km heading 12 degrees north of west. How far west have you gone? How far north?

Closure Answer on your whiteboard: You drive 2.4 km heading 12 degrees north of west. How far west have you gone? How far north? 2.4km(cos(12)) = 2.3km west 2.4km(sin(12)) = .50km north