SOLUTION: Hi, There's a word problem on vectors that I've been having trouble with: "What direction and airspeed are required for a plane to fly 400 miles due north in 2.5 hours if the wi

Algebra ->  Vectors -> SOLUTION: Hi, There's a word problem on vectors that I've been having trouble with: "What direction and airspeed are required for a plane to fly 400 miles due north in 2.5 hours if the wi      Log On


   

Question 1179989: Hi,
There's a word problem on vectors that I've been having trouble with: "What direction and airspeed are required for a plane to fly 400 miles due north in 2.5 hours if the wind is blowing 11 mph in the direction of 58° east of north?" I'm not sure where to start and how to draw a diagram to represent the problem and I'd love for some help on it!
Thank you!
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
The resultant vector will have direction due north and magnitude equal to the
speed: 400 mi/2.5 h = 160 miles per hr
The air speed and heading of the plane must be able to counteract the speed
and direction of the wind. The direction of the wind is 58 deg E of N, which
is 32 deg N of E. The plane must head west of north to counteract this. Adding
the vectors head to tail, we get the resultant vector. The coordinates of the
end point of the resultant vector are given by (x,y) = (-11cos(32),160-11sin(32))
Thus the air speed is given by sqrt(x^2+y^2) = 154.45
The direction is given by atan(x/y) = -3.46 deg, or 3.46 deg W of N
Ans: speed = 154.45 mph, direction 3.46 deg W of N
See attached diagram.