This question appeared on Bangladesh physics Olympiad 2014, Sylhet, Bangladesh for students of class 9 and 10.
I really tried to solve this, but I failed. Please help.
Suppose that, while lying on the beach near the equator watching the sun set over a calm ocean, you start a stopwatch just as the top of the sun disappears. You then stand, and fitting your eyes by a height $H=1.70\,\mathrm m$, and stop the watch when the top of the sun again disappears. If the elapsed time is $T=574\,\mathrm s$, what is the radius of the Earth?
You can check out the question: http://bdpho.org/pdf/sylhet_cat%20B_2014.pdf The question is on number 7.