What Are the Correct Components of a 20km Displacement at N30°E?

[bobby_burke]

A boat sails in a straight line 20km [N30°E]. What are the components of its displacement to the north and east?

the answers given are 17 km [N] and 10 km [E], but using the formulae
Ay = A Sin σ and Ax = A Cos σ, I've got the values mixed up... could it be because I've drawn it wrong? I've got it drawn as 30° North of East... Does N30°E mean 30° east of north?

 

[bigbeau]

hey Bobby,

yes, it does mean 30 degrees east of north. therefore your sigma value is 60 deg instead of 30.
that should fix you

Beau

 

[kyle8921]

Yes, N30°E means 30° east of north. The components of a vector are the parts that make up the vector's magnitude and direction. In this case, the magnitude is 20km and the direction is N30°E. To find the components, we can use the trigonometric formulas you mentioned: Ay = A Sin σ and Ax = A Cos σ. In this case, A represents the magnitude (20km) and σ represents the direction (30°).

To find the component to the north, we use Ay = 20km * Sin 30° = 10km [N]. This means that 10km of the boat's displacement is in the north direction.

To find the component to the east, we use Ax = 20km * Cos 30° = 17.32km [E]. This means that 17.32km of the boat's displacement is in the east direction.

It is possible that you may have drawn the vector incorrectly, which could have resulted in the mixed up values. Make sure to double check your drawing and use the correct values for the magnitude and direction when using the trigonometric formulas.