A stone is dropped into a lake from a tower $500\, metre$ high. The sound of the splash will be heard by the man approximately after ..... $\sec$
Diffcult
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(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 .$
${t_1} = \sqrt {\left( {\frac{{2h}}{g}} \right)} = \sqrt {\left( {\frac{{2 \times 500}}{{10}}} \right)} = 10\,sec$ (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 .$
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