Question

A plane is flying on a bearing of 51 east of south at 542 mph. A tail wind is adding to the plane's velocity and blowing 83 west of north at 86 mph. Determine the direction of the plane

Answer 1

Are you working on vectors?

Answer 2

yes

Answer 3

Change the velocities to aI +bJ vectors (I,J) being the unit vectors in the x and y direction respectively. Let me give this a shot on the first one, then you can finish it.

Answer 4

51 east of south is the same as 39 south of east. So that makes our airplane vector (vector P)

vector P = 542(cos 39 (I) -sin 39 (J))

where (I) and (J) are the unit vectors in the x and y directions respectively. The minus sign on the (J) vector is due to the bias in the southerly direction.

Answer 5

Vector W is similar, but keep in mind that the wind is given where it is coming from, so in terms of where it is going, we can convert it to seven degrees south of east. That gives us

vector W = 86(cos 7 (I) - sin 7 (J))

Answer 6

From here, add the vectors. Got it?

Answer 7

kk, Though can you write out the process in one message..just to make sure I have it right

Answer 8

Draw the pictures, and it will be clear how it works. Sorry but the drawing thing is one of my many online limitations

Answer 9

Maybe somebody else can help you with a picture.