Everything Science Grade 11

11.8 CHAPTER 11. VECTORS

10 m

6 m

8 m

α

The magnitude of the resultant, R is 10 m. So all we haveto do is calculate

its direction. We can specify the direction as the angle the vectors makes with a

known direction. To dothis you only need to visualise the vector as starting at

the origin of a coordinate system. We have drawn this explicitly belowand the

angle we will calculateis labelled α.

Using our known trigonometric ratios we can calculate the value of α;

tan α =

6m

8m

α = tan−^1

6m

8m

α = 36, 8 o.

Step 6 : Quote the final answer

R� is 10 m at an angle of 36 , 8 ◦to the positive x-axis.

Exercise 11 - 5

1. Harold walks to school by walking 600 m Northeast and then 500 mN 40 oW. Determine his
   resultant displacement by means of addition of components of vectors.


2. A dove flies from her nest, looking for foodfor her chick. She fliesat a velocity of 2 m·s−^1 on
   a bearing of 135oin a wind with a velocity of 1,2 m·s−^1 on a bearing of 230o. Calculate her
   resultant velocity by adding the horizontal and vertical components of vectors.

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(1.) 00na (2.) 00nb

Extension: Vector Multiplication