Question

An areoplane files from P and Q with speed v and then from Q and P with the same speed. If wind blows normal to straight line PQ with the speed V, the total time for to and for motion is

• A. $\frac{L}{\left( v^{2} - V^{2} \right)^{1/2}}$
• B. $\frac{2L}{\left( v^{2} - V^{2} \right)^{1/2}}$
• C. $\frac{2L}{V - v}$
• D. $\frac{2L}{\left( v^{2} - V^{2} \right)}$

Answer 1

Answer: (B)

$\frac{2L}{\left( v^{2} - V^{2} \right)^{1/2}}$

Answer 2

The aeroplane has to follow a path such that resultant of v and V should be in line with PQ

Thus R = $\sqrt{v^{2} - V^{2}}$ time taken to cover distance PQ = L/$\sqrt{v^{2} - V^{2}}$

Since velocity is the same during return also/time taken to cover distance QP = L/$\sqrt{v^{2} - V^{2}}$.

Thus, total time = L/$\sqrt{v^{2} - V^{2}}$