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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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.
Θ = 53º
Now, could the boy end up with the same displacement by taking a different path?
Θ = 37º
As you can see, the boy traveled in different directions, but ended up in the same spot as before.
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
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.
To find Vx (Horizontal Component)
Cos Θ = adj / hyp
Cos 30º = Vx / 20 m/s
V = 20 m/s
Vx = 17.3 m/s
To find Vy (Vertical Component)
Θ = 30º
Sin Θ = opp / hyp
Sin 30º = Vy / 20 m/s
Vx = 10 m/s
Think of thing this way. First you were asked to solve:
Now you are being asked to do things in reverse order.