Question

Two aeroplanes fly from their respective positions 'A' and 'B' starting at the same time and reach the point 'C' (along straight line) simultaneously when wind is not blowing. On a windy day they head towards 'C' but both reach the point 'D' simultaneously in the same time which they took to reach 'C'. Then the wind is blowing in

(A) North-West direction
(B) North-East direction
(C) Direction making an angle $0 < \theta < {90^0}$ (but not ${45^0}$) with North towards West
(D) North direction

Answer 1

The aircraft moves through the air at some velocity called the airspeed. The air moves at some constant velocity called the wind speed which is perpendicular to the airspeed. The airspeed and the wind speed are both vector quantities having a magnitude and a direction. The chief effect of the cross wind is to deflect the flight path in the direction of the wind.
When aeroplane is moving in the air, the velocity and direction of the plane is affected by the direction and speed of the wind. In question, when two planes simultaneously meet at Point ‘C’, no presence of wind is assumed. At present of wind, they do not meet at point ‘D’ simultaneously.
In question, first of all, the vector form of two aero planes will be calculated. Then for the second case vector sum of wind velocity and second aero plane velocity will be calculated.

Complete step by step answer:
When 2 aero plane reach simultaneously at ‘C’, Let$V(a) = V\hat i$ & $V(b) = \dfrac{V}{2}\hat i + \dfrac{V}{2}\hat j$, i &j; being unit vectors along East & North respectively.
Let $V(w) = a\hat i + b\hat j$.
$V(b) + V(w)$ has no component along east
Hence $a = \left( { - \dfrac{V}{2}} \right)$.
$V(a) + V(w) = (V + a)\hat i + b\hat j$.
As 'A' moves along north east, it's components along north and east are equal.
Hence $V + a = b$,
Hence $b = \dfrac{V}{2}$.
So, we get, velocity of wind, $V(w) = \left( { - \dfrac{V}{2}} \right)\hat i + \dfrac{V}{2}\hat j$

So, the correct answer is “Option A”.

Additional Information:
For aero plane motion in air, all of Newton’s laws of motion are connected. For every motion, every one of Newton’s laws applies.
The first law shows that the plane will keep flying at the same speed unless something makes it accelerate.
The second law shows that we must add up the force to lift, weight, drag and thrust and take into account the mass of the plane to determine which direction and how fast the plane is accelerating.
The third law shows that there will be an opposite reaction for every movement the plane is making. Generally the air moves as a result of this reaction.

Note:
Be careful while taking unit vectors of velocities of wind and two aeroplanes. First draw a diagram according to the question. This may help with calculating the required parameters asked in question. An important point is that, if we don’t take the right sign of the velocity component, then the answer will be incorrect. In question, sign of x and y components of velocity plays an important role to determine accurate direction of resultant velocity.