a
(a) The time taken by the stone to reach the lake

\({t_1} = \sqrt {\left( {\frac{{2h}}{g}} \right)} = \sqrt {\left( {\frac{{2 \times 500}}{{10}}} \right)} = 10\,sec\) (Using \(h = ut + \frac{1}{2}g{t^2}\))

Now time taken by sound from lake to the man \({t_2} = \frac{h}{v} = \frac{{500}}{{340}} \approx 1.5\sec \)

==> Total time \( = {t_1} + {t_2} = 10 + 1.5 = 11.5\sec .\)