an airplane P is heading N80W at 250m/s relative to the air.the wind blows from N10E with the speed of 40m/s relative to the ground. Find the magnitude and direction of the velocity of airplane P relative to the ground.In the meantime, the velocity of airplane Q relative to the air is 250 m/s in the direction of N20W. What is the speed of airplane Q relative to airplane P?

Question

an airplane P is heading N80W at 250m/s relative to the air.the wind blows from N10E with the speed of 40m/s relative to the ground.  Find the magnitude and direction of the velocity of airplane P relative to the ground.In the meantime, the velocity of airplane Q relative to the air is 250 m/s in the direction of N20W. What is the speed of airplane Q relative to airplane P?

phi · Answer

wind blows from N10E with the speed of 40m/s relative to the ground.
This fixes a previous post which had the wind blowing the wrong way.

anonymous · Answer

why 40m/s negative?

phi · Answer

wind blows from N10E 
the other vectors are heading in the direction given.  Wind is heading opposite to this.  we could do 180 degrees from this direction, but minus does the same thing

anonymous · Answer

is it final answer we need to calculate the ratio?

phi · Answer

What is the speed of airplane Q relative to airplane P?
that is the ratio of the length of vector Q' (i.e. Q+Wind) to the length of vector P' (P+Wind)

anonymous · Answer

thanx, now i understand it..

anonymous · Answer

is it true the direction of p is -0.91?

phi · Answer

First, P is given in terms of North:   P is heading N80W
So you know P.  Are you asking about P'  (P + Wind)?

anonymous · Answer

no,i ask direction of p? is it true i take Q'/P'?
and i get the answer=-0.91.. i think it's wrong..

phi · Answer

OK, you are answering
Find the magnitude and direction of the velocity of airplane P relative to the ground.
which is what I am calling P2 (affected by the wind)|dw:1329156568420:dw|
magnitude is 253.18 m/s

direction is: