Vector calculus and flight path

[diana7]

A pilot flies with a heading of 160 degrees and an airspeed of 250km/h.

a)how long should it take the pilot to fly to a town that is 1200km away on the heading he has chosen

b) there is a steady wind of 30km/h from the drection 030 degrees. Calculate the ground velocity

c) How far, and in what direction from the town, is the plane after the amount of time from part a)?

I got a) and b) already, i just don't understand c).
a) 4.8h
b) 270 km/h S15E
c) ?

 

[zhermes]

The direction he is heading (pointing) is 160 degrees, and along that line is the town. Because of the wind, he is actually moving in a different direction (which you found in 'b'). So the pilot is not going to perfectly reach the town, after the amount of time in 'a', where will he ACTUALLY be? and then, how far away is that, from where the town is?

 

[diana7]

I still don't understand.

Are we suppose to have a new vector? And what would the magnitude be? Then I have to find the resultant from the town to the final destination?

 

[zhermes]

You already have the velocity vector (relative to the ground), you just need to convert it into a displacement vector--to figure out where he'll actually end up in a certain amount of time ('a'). Then yes, you're right: you find the resulting displacement between the final destination and the town.