Solving Vector Addition with Wind and Velocity

[StatGuy2000]

1. An air ambulance is traveling from Barrie to Toronto. Toronto is located 90 km (S 5° E) of Barrie. If the wind is blowing from the South with a velocity of 62 km/h, and the plane's air speed is 375 km/h, what direction must the pilot fly to make it to Toronto?



2. Let u=<u_{1},u_{2}>, v=<v_{1},v_{2}> be vectors and let k be a scalar. Then u+v=<u_{1}+v_{1},u_{2}+v_{2}> and ku=<ku_{1},ku_{2}>.

||u|| = √(u^{2}_{1}+u^{2}_{2})

u = ||u||(cos θ)i + ||u||(sin θ)j

tan θ = sin θ / cos θ





3. I tried vector addition but I'm just stumped (my cousin is taking a high school calculus course, and I volunteered to help him out).

 

[LCKurtz]

It looks like you are just listing random formulas.

I'll help you set it up since you are helping someone else. Call the wind vector $\vec W = \langle 0,62\rangle$. Let $\theta$ be the polar coordinate (unknown) angle the plane flies, so the plane vector is $\vec P = \langle 375\cos\theta,375\sin\theta\rangle$. You want the resultant vector for the plane and wind to be in the direction of the town, say $\vec D = \langle \cos(-85^\circ),\sin(-85^\circ)\rangle$. So set up the equations $\vec P + \vec W = k\vec D$ and use the two component equations to solve for $\theta$.

 

[StatGuy2000]

Hi LCKurtz,

Thanks for all your help! As far as listing formulas, I was looking at all relevant formulas from my cousin's algebra textbook -- as a professional statistician, I admit to being rather embarrassed that I had trouble with this question!