How Do You Calculate Resultant Velocity in Vector Addition?

[jord12321]

Homework Statement

A plane heads 20° north of east at 200 m/s. The wind blows 60° north of east at 50 m/s. What is the resultant velocity of the plane?

Homework Equations

Δv= v2-v1 or Δv= v2+(-v1)

The Attempt at a Solution

I know you have to solve for the x and y, but I don't know how to do that. Then I know once you get your two answers, you use pythagorean theorem to get the final answer.

 

[gb7nash]

First off, every vector in 2D has an x component and a y component. How do you find the x and y component for a given vector?

 

[jord12321]

You use sinΘ or cosΘ, and then you times that number by the velocity.

 

[gb7nash]

You use sinΘ or cosΘ, and then you times that number by the velocity.

Ok...so do it and show what the x and y components are of the plane and the wind.

 

[iRaid]

Once you get what he says add the x components and y components vectorally.

 

[jord12321]

So my total for x was 111 and for y it was 213. So then I used pythagorean theorem and got 240. I'm not sure if this is correct though. And then for my angle i got 62.5

 

[gb7nash]

So my total for x was 111 and for y it was 213. So then I used pythagorean theorem and got 240. I'm not sure if this is correct though. And then for my angle i got 62.5

You got your sin and cos mixed up. x = rcosΘ and y = rsinΘ. Besides that, do what you were doing.

Also, in the future, show your work. I'm lucky to have a calculator handy, so I can tell where you made your mistake, but it's easier to follow your work than trying to decipher what you did.