Geometry
posted by Pauline .
In what direction must a plane head if it can maintain 350 km/h in still air, wishes to fly 500km in a diirection 040degree and the wind is blowing at 56km/h from 100 degree? howlong would the journey take(to the nearest minutes)? how long would the return journey take, again to the nearest minutes, if the wind is still 56km/h from 100 degree?
I drew the following diagram.
OX is the xaxis, and OY is the yaxis
OB is the desired vector you want to go
so angle(YOB)=40º, it has a magnitude of 500.
Let OA be the vector the plane has to fly, AB is the vector representing the direction and velocity of the wind.
(point A is to the right of B and slightly downwards so it makes a 10º angle with the horizonatal)
Using a bit of basic geometry it should be easy to follow that angle(OBA)=120º
If we let the time taken be t hours, we can label the maginitude of AB as 56t and the magnitude of OA as 350t
Using the cosine law I got the equation
(350t)^2 = 500^2 + (56t)^2  2(500)(56t)cos 120º
or
119364t^2  28000t  250000=0
check my arithmetic but by the quadratic formula I got t=1.56 or (a negative t, which we reject)
So the time taken is 1.56 hours
=1.56*60 minutes
=94 minutes to the nearest minute.
Using the Sine Law, Sin(BOA)/(56*1.56) = sin 120/(350*1.56)
sin(BOA)=.1385
angle(BOA)=7.96º
so the direction should be 40º + 7.96º
or appr 48º
Setting up a similar geometrical figure you should be able to do the second part yourself.
Respond to this Question
Similar Questions

physics
An airplane flies at airspeed (relative to the air) of 400km/h. The pilot wishes to fly due North (relative to the ground) but there is a 110km/h wind blowing Southwest (direction 225º clockwise from North). In what direction should … 
Physics
a plane can fly at 200km/h in still air and has to reach a destination 600km northeast. a 50km/h wind blows from the west. in which direction must the plane head? 
physics
An airplane pilot wishes to fly due west. A wind of 82.0 km/h is blowing toward the south. If the airspeed of the plane (its speed in still air) is 380.0 km/h, in which direction should the pilot head? 
physics
An airplane pilot wishes to fly due west. A wind of 82.0m/s is blowing toward the south.If the airspeed of the plane (its speed in still air) is 375.0 km/h, in which direction should the pilot head? 
Physics
An airplane needs to fly due south. The plane can fly at a speed of 720.0 km/hr in still air. If there is a wind blowing to the northeast at 70.0 km/hr, in what direction should the plane fly to maintain its heading of due south? 
Physics
The piolt of an airplane wishes to fly due north, but there is a 65km/h wind blowing toward the east. in what direction should the pilot head her plane if its speed relative to the air is 340 km/h? 
physics
The pilot of an airplane wishes to fly due north, but there is a 71 km/h wind blowing toward the east. (a) In what direction should the pilot head her plane if its speed relative to the air is 314 km/h? 
mastering physics
An airplane pilot wishes to fly due west. A wind of 90.0 km/h is blowing toward the south.If the airspeed of the plane (its speed in still air) is 305.0 km/h , in which direction should the pilot head? 
algebra
With an 80 km/h head wind a plane can fly a certain distance in 4 h. Flying in the opposite direction, with the same wind blowing, it can fly that distance in one hour less. What is the plane’s speed? 
Physics
An airplane pilot wishes to fly due west. A wind of 80km/hr is blowing towards the south. a) If the speed of llane in air is 320km/hr, in which direction should the pilot head?