Everything Science Grade 11

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