On morning Joy was walking on a grass-way in a garden.Wind was also blowing in the direction of his walking with speed `u`.He suddenly saw his friend Kim walking on the parallel grass-way at a distance `x` away.Both stopped as they saw each other when they were directly opposite on their ways at a distance `x`.Joy shouted "Hi Kim".Find the time after which Kim would have heard his greeting.Sound speed in still air is `v`.

Options

A. `x/sqrt(v^(2)-u^(2))`
B. `(2x)/sqrt(v^(2)-u^(2))`
C. `(x)/(2sqrt(v^(2)-u^(2)))`
D. `(x)/(4sqrt(v^(2)-u^(2)))`

Answer

A

Explanation

The situation is shown in figure.When Joy shouted, the sound which is going directly toward Kim will not reach her as due to wind drift is added to it.The sound which is going in the direction at an angle `theta`,to their line joining will reach to Kim as when drift is added to it as shown in figure, the resultant is in the direction of their line joining.
The resultant velocity of sound is `v_(R)=sqrt(v^(2)-u^(2))`
Time taken by sound to reach Kim is `t=x/sqrt(v^(2)-u^(2))`