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 was 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 $0<\theta <{90}^o$ (but not ${45}^o$) with North towards West.
• D. North direction

Answer 1

Answer: (A)

North-West direction

Let V(a) = Vi & V(b) = V/2 i + V/2 j (as both reach simultaneously at 'C'), i &j being unit vectors along East & North respectively. Let V(w) = a i + b j. V(b) + V(w) has no component along east hence a = (-V/2). V(a) + V(w) = (V+a)i + b j . As 'A' moves along north east, it's components along north and east are equal. Hence V+a = b, hence b = V/2. Hence V(w) = -V/2 i + V/2 j Hence option 'A'