Vectors and Components-Part One

[Medgirl314]

Homework Statement

An aircraft is traveling at 200 mi/h on a heading of 38 degrees. Find the northerly and easterly components of its velocity.

Homework Equations

Sine=opposite/hypotenuse
Cosine=adjacent/hypotenuse

The Attempt at a Solution

The problem states that the angle given is a heading. In order to use our equations, it is best to convert to our non-heading angle. I don't know what that's called, but it's 52 degrees. So to find the northerly component, I did 200cos(52) and got 123.1 mi/h. To get the easterly component, I did 200sin(52) and got 157.6 mi/h. Are these the right answers so far? Do I need to convert back to a "heading" answer? How would I do that?


Thanks so much for a helpful and descriptive answer!

 

[PhanthomJay]

Homework Statement

An aircraft is traveling at 200 mi/h on a heading of 38 degrees. Find the northerly and easterly components of its velocity.

Homework Equations

Sine=opposite/hypotenuse
Cosine=adjacent/hypotenuse

The Attempt at a Solution

The problem states that the angle given is a heading. In order to use our equations, it is best to convert to our non-heading angle. I don't know what that's called, but it's 52 degrees. So to find the northerly component, I did 200cos(52) and got 123.1 mi/h. To get the easterly component, I did 200sin(52) and got 157.6 mi/h. Are these the right answers so far? Do I need to convert back to a "heading" answer? How would I do that?


Thanks so much for a helpful and descriptive answer!

A heading in aviation terms is measured clockwise frpm magnetic north. If the airplane is heading 38 degrees, it means it is moving in a direction 38 degrees east of north, that is, in a generally northeast direction. The problem should more specifically state or sketch the heading, often denoted for this case as N 38 E. in which case , the northerly component of the velocity is 200 cos 38 or 200 sin 52, whichever triangle you choose(draw a sketch!).

 

[Medgirl314]

Okay, I think I got all that. :-) I forgot to mention that I already drew a diagram. The problem isn't any more specific than I indicated, unfortunately. Are you stating that my answer for the northerly component is correct?

Thank you!

 

[PhanthomJay]

Okay, I think I got all that. :-) I forgot to mention that I already drew a diagram. The problem isn't any more specific than I indicated, unfortunately. Are you stating that my answer for the northerly component is correct?

Thank you!

Your answer is incorrect. The plane is heading 038 degrees per its compass reading at a speed of 200 mph. Its northerly component is 200 cos 38, not 200 cos 52. Please look at your sketch again to confirm this result.

 

[Medgirl314]

I think I see what you're saying. I should have made my sketch larger and neater. I got it backwards, right? It would be 200 sin 52 if I were to use the this angle, correct?

 

[PhanthomJay]

I think I see what you're saying. I should have made my sketch larger and neater. I got it backwards, right? It would be 200 sin 52 if I were to use the this angle, correct?

Correct!

 

[Medgirl314]

So the northerly component is 157.6 mi./h. Thank you! Was the easterly component correct?

 

[PhanthomJay]

So the northerly component is 157.6 mi./h. Thank you! Was the easterly component correct?

Why no the easterly component is incorrect...what should it be ?

 

[Medgirl314]

Is is 123.1 mi./h? Just for clarity, I got the right answer for the northerly component, correct?

Thanks!

 

[PhanthomJay]

Is is 123.1 mi./h? Just for clarity, I got the right answer for the northerly component, correct?

Thanks!

Yes both values for the northerly and easterly components are now correct. ( You might want to round them off however at least to the nearest whole number with no decimal point. ).

 

[Medgirl314]

So just 158 mi/h and 123 mi/h. Thank you!