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Vector Components. Vector Components. In past lessons we learned how to add two vectors. For example a boy walks 9m north than 12m east. His displacement turns out to be 15m @ 53º E of N. 12 m. Finish. 9 m. Θ = 53º. 15 m. Start. Vector Components.

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vector components2
Vector Components

In past lessons we learned how to add two vectors.

For example a boy walks 9m north than 12m east. His displacement turnsout to be 15m @ 53º E of N.

12 m

Finish

9 m

Θ = 53º

15 m

Start

vector components3
Vector Components

Now, could the boy end up with the same displacement by taking a different path?

Finish

15 m

9 m

Θ = 37º

Start

12 m

As you can see, the boy traveled in different directions, but ended up in the same spot as before.

vector components4
Vector Components

As it turns out, the boy could have taken an infinite number of routes to endup in the same spot.

This implies a resultant (the addition of two or more vectors) can be resolved into an infinite number of components or parts.

Luckily for us, engineers are mostly concerned with only two of these components or parts:

Horizontal and Vertical Components

vector components5
Vector Components

Example: A soccer player kicks a ball with a velocity of 20 m/s at an angleof 30º with respect to the horizontal. What is the balls horizontal and verticalvelocities?

V = 20 m/s

Θ = 30º

To solve these types of problems we must use SOH CAH TOA.

vector components6
Vector Components

To find Vx (Horizontal Component)

hyp

Cos Θ = adj / hyp

Cos 30º = Vx / 20 m/s

V = 20 m/s

Vy =

10 m/s

Vx = 17.3 m/s

opp

To find Vy (Vertical Component)

Θ = 30º

adj

Vx =

17.3 m/s

Sin Θ = opp / hyp

Sin 30º = Vy / 20 m/s

Vx = 10 m/s

vector components7
Vector Components

Think of thing this way. First you were asked to solve:

B

A

+

B

=

C

A

C

Now you are being asked to do things in reverse order.

B

C

=

A

+

B

A

C