Everything Science Grade 11

(Marvins-Underground-K-12) #1

11.8 CHAPTER 11. VECTORS


Example 11: Adding Vectors UsingComponents


QUESTION

If in Figure 11.4,A� = 5,385m at an angle of 21.8◦to the horizontal andB� = 5m at an angle
of 53,13◦to the horizontal, findR�.

SOLUTION

Step 1 : Decide how to tackle the problem
The first thing we mustrealise is that the orderthat we add the vectorsdoes not
matter. Therefore, we can work through the vectors to be added in any order.

Step 2 : ResolveA� into components
We find the components ofA� by using known trigonometric ratios. First we find
the magnitude of the vertical component, Ay:

sin θ =
Ay
A
sin21, 8 ◦ =
Ay
5 , 385
Ay = (5,385)(sin21, 8 ◦)
= 2m

Secondly we find the magnitude of the horizontal component, Ax:

cos θ =

Ax
A
cos21. 8 ◦ =

Ax
5 , 385
Ax = (5,385)(cos21, 8 ◦)
= 5m

5,385 m

5 m

2 m

The components give the sides of the right angle triangle, for whichthe
original vector,A�, is the hypotenuse.

Step 3 : ResolveB� into components
We find the components ofB� by using known trigonometric ratios. First we find
the magnitude of the vertical component, By:

sin θ =
By
B
sin53, 13 ◦ =
By
5
By = (5)(sin53, 13 ◦)
= 4m
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