Answer to Question #123862 in Mechanics | Relativity for ravi tetarwal

Question #123862
You drop a rock into a well and count the seconds before you hear a splash. If you counted 10 seconds before you heard the splash, how deep is the well?
1
Expert's answer
2020-06-25T09:35:05-0400

Let hh be the depth of the well. 10 seconds is the time for rock to fall to water and for sound to travel to us.

h=gt122,      h = \dfrac{gt_1^2}{2}, \;\;\; h=cst2,      t1+t2=10s.h = c_st_2, \;\;\; t_1+t_2=10\,\mathrm{s}.

Therefore, gt12=2cst2,    t2=10t1.gt_1^2=2c_st_2, \;\; t_2=10-t_1. So gt12=2cs(10t1).gt_1^2=2c_s(10-t_1). Solving this equation, we get t1=8.8s,  t2=1.2s,h396m.t_1=8.8\,\mathrm{s}, \; t_2 = 1.2\,\mathrm{s}, h \approx 396\,\mathrm{m}.

We may notice that the time interval is quite large, so the well has significant depth.


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