Question

An aeroplane flies along a straight line from A to B with a speed $v$${}_0$ and back again with the same speed $v$${}_0$. A steady wind $v$ is blowing. If $AB=l$ then

• A. total time for the trip is $\frac{2v_{0}l}{v_0^2-v^2}$ if wind blows along the line AB
• B. total time for the trip is $\frac{2l}{\sqrt{v_0^2-v^2}}$, if wind blows perpendicular to the line AB
• C. total time for the trip decrease because of the presence of wind
• D. total time for the trip increase because of the presence of wind

Answer 1

Answer: (A), (B), (D)

total time for the trip is $\frac{2v_{0}l}{v_0^2-v^2}$ if wind blows along the line AB
total time for the trip is $\frac{2l}{\sqrt{v_0^2-v^2}}$, if wind blows perpendicular to the line AB
total time for the trip increase because of the presence of wind

Wind increases time. That is always true. Hence option D is correct
Option A.=> time $=\frac{l}{(v_0+v)}+\frac{l}{(v_0-v)}=\frac{2v_{0}l}{(v_0^2-v^2)}$
option B => velocity along the line = $\sqrt{v_0^2-v^2}$ for both ways.

Hence time = $\frac{2l}{\sqrt{v_0^2-v^2}}$