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Copyright © by Holt, Rinehart and Winston. All rights reserved. Objectives Distinguish between a scalar and a vector. Add and subtract vectors by using.

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Presentation on theme: "Copyright © by Holt, Rinehart and Winston. All rights reserved. Objectives Distinguish between a scalar and a vector. Add and subtract vectors by using."— Presentation transcript:

1 Copyright © by Holt, Rinehart and Winston. All rights reserved. Objectives Distinguish between a scalar and a vector. Add and subtract vectors by using the graphical method. Multiply and divide vectors by scalars.

2 Copyright © by Holt, Rinehart and Winston. All rights reserved. Scalars and Vectors

3 Copyright © by Holt, Rinehart and Winston. All rights reserved. Scalars and Vectors

4 Copyright © by Holt, Rinehart and Winston. All rights reserved. Graphical Addition of Vectors

5 Copyright © by Holt, Rinehart and Winston. All rights reserved. Triangle Method of Addition

6 Copyright © by Holt, Rinehart and Winston. All rights reserved. Properties of Vectors

7 Copyright © by Holt, Rinehart and Winston. All rights reserved. Subtraction of Vectors

8 Copyright © by Holt, Rinehart and Winston. All rights reserved. Multiplication of a Vector by a Scalar

9 Copyright © by Holt, Rinehart and Winston. All rights reserved. Graphical Addition of Vectors List given information Set an appropriate scale (i.e. 1cm = 25 km) Draw first vector to scale to establish frame of reference Draw subsequent vectors with the tail starting at the tip of the previous  Be sure to retain proper direction of each vector Resultant is drawn from the tail of the first to the tip of the last  Measure resultant and calculate its magnitude using the scale.  Measure the angle of the resultant and use it to specify direction

10 Copyright © by Holt, Rinehart and Winston. All rights reserved.  x 1 = 420 m @ 90 o (East) 30 o xrxr Add. 90 o 270 o 0o0o 180 o  x 2 = 280 m @ 60 o (30 o North of East)  x 1 (8.4 cm)  x r = 680 m  1 cm = 50 mscale:  x 2 (5.6 cm) measure length in cm measure angle (say 12°) @ 12 o North of East (say, 13.6 cm)

11 Copyright © by Holt, Rinehart and Winston. All rights reserved. v 1 = 53 km/h @ 295 o Add. v r (6.6 cm) v r = 66 km/h  = 115° 1 cm = 10 km/hscale: v 1 (5.3 cm) v 2 (3.2 cm) @ 245 o v 2 = 32 km/h @ 250 o v 3 = 45 km/h @ 155 o v 3 (4.5 cm) 90 o 0o0o 0o0o 270 o 0o0o 180 o 0o0o

12 Copyright © by Holt, Rinehart and Winston. All rights reserved. d 1 = 1160 km @ 20 o Add. 0o0o 180 o 90 o 270 o drdr d r = 1300 km  1 cm = 100 kmscale: d1d1 d2d2 @ 12 o d 2 = 470 km @ 300 o d 3 = 280 km @ 110 o d3d3 0o0o 90 o 0o0o 0o0o

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