story problem involving vectors

A plane is flying in the direction 290 degrees ( measured clockwise from north). Its airspeed is 800 km/ hr. The wind at the planes altitude is blowing in the direction 150 degrees ( measured clockwise from north) at 100 km/ hr. what is the true direction ( measured clockwise from north) and ground speed of the plane?

This is what i have so far

for the boat vector

$\displaystyle \vec{p} = 800 < cos 290^0, sin 290^0 > $

for the wind vector

$\displaystyle \vec{w} = 100 < cos 150^0, sin 150^0 > $

vector t for the true coarse of plane.

After multiplying and adding both cos and sin of both vectors i have:

$\displaystyle \vec{t} = < 187.013, - 701.754 > $

that would put me in the third quadrant?

i need to find the angle?

$\displaystyle \theta = tan^-1 \frac{ -701.754}{187.013} = - 76.030 ^0$

at this point do i subtract 180^0?

Re: story problem involving vectors

Re: story problem involving vectors

Unless my solution and interpretation of the problem were wildly off (they could be), this doesn't belong in the calculus section. Ignoring that, here is my solution, assuming my interpretation of the problem was correct:

Since the degrees are measured clockwise from the North you have (converted into standard degrees):

Plane: $\displaystyle \vec{p} = \langle 800, 160$^{\circ}$\rangle $

Wind: $\displaystyle \vec{w} = \langle100, 300$^{\circ}$\rangle $

From here it seems you need to find $\displaystyle \vec{p} + \vec{w} $ to find the true speed and direction of the plane. We do this by decomposing the vectors.

$\displaystyle \vec{p}: (800cos(160$^{\circ}$), 800sin(160$^{\circ}$)) \approx (-751.754, 273.616) $

$\displaystyle \vec{w}: (100cos(300$^{\circ}$), 100sin(300$^{\circ}$)) = (50, -50\sqrt3) $

Through simple addition we get:

$\displaystyle \vec{t} \approx (-701.754, 187.014) $

I don't have time to finish this but from here just convert back into standard vector notation. The radius will be the groundspeed and the angle (be sure to convert back into the original From-the-North angle definition) will be your true direction.

Re: story problem involving vectors

thank you but this was a problem in my calculus 3 class.