What Heading and ETA Will Get Me to City B?

[Gebraroest]

Homework Statement

A pilot wishes to fly form city A to city B, a distance of 720 km on a bearing of 070°. The speed of the plane is 700 km/h. An 60 km/h wind is blowing on a bearing of 110°. What heading should the pilot take to reach his or her destination? How long will the trip take? Use Cartesian vector methods to solve all problems.

Homework Equations

The Attempt at a Solution

the Cartesian vector of the plane is
=[700 cos(20°).700 sin(20°)]
=[658,239]

the Cartesian vector of the wind is
=[60 cos(20°),-700 sin(20°)]
=[56,-21]

I have no idea what to do now, any help is greatly appreciated

 

[hunt_mat]

If there were no wind then the plane could fly in the direction [658,239] without a problem, now as there is a wind in the direction [56,-21]. Now the idea here is to draw a triangle of vectors from "head" to "tail", the sum of which is zero. Let [x,y] be the speed that the plane will fly to compensate for the wind, then the following holds [658,239]+[x,y]+[56,-21]=0, from here you can work out the direction.

 

[mege]

First, before you go too much further, I highly suggest verifying your vectors. You shouldn't have a value for the direction of the plane (that's what you're solving for first!). You should have 1 complete vector (wind) and 2 partial vectors (resultant and plane).

Second, I disagree with hunt_mat's approach (because you have two unknowns - the plane's direction isn't known). Once you know the resultant vector (by solving for it's direction) you can find its 'new' speed and that can be used to find it's ETA.