# Vector question

1. May 11, 2014

### cosmictide

Hi,

I'm not really sure whether I've answered this question correctly. I'd really appreciate if someone could check my answers and point me in the right direction if I'm indeed incorrect.

1. The problem statement, all variables and given/known data

An aircraft has an air speed (speed relative to the surrounding air) of 680 km h-1 and a heading of 150°. There is a wind blowing from a bearing of 220° at a speed of 70 km h-1. Take i to point east and j to point north.

a) Express the velocity p of the aircraft relative to the air and the velocity w of the wind in component form, giving numerical values in km h-1 to one decimal place.

b) Express the resultant velocity v of the aircraft in component form.

c) Hence find the magnitude and direction of the velocity v of the aircraft,giving the magnitude to the nearest km h-1 and the direction as a bearing to the nearest degree.

3. The attempt at a solution

a) p=340 km h-1 i-588.9 km h-1 j and w=53.6 km h-1 i+45 km h-1 j.

b) v=286.4 km h-1 i-633.9 km h-1 j.

c) Magnitude of v=696 km h-1 (to the nearest km h-1) and the direction of the velocity v=294° (to the nearest degree).

Thanks.

2. May 11, 2014

### jackarms

Your numbers look good, but I think you have some of the signs mixed up. Look at the angles you're given -- the plane's direction is 150 degrees, so this would mean a negative i vector and a positive j vector. For the wind, if it points toward 220 degrees, then both vectors would be negative.

3. May 11, 2014

### cosmictide

Hi,

Thank you for your reply. The angles were measured clockwise rather than anticlockwise which is the norm but that shouldn't matter. Also the wind was blowing from a bearing of 220° so would travel in the opposite direction for instance a southerly wind blows towards the north.

Thanks.