Question

Suppose that, while lying on a beach near the equator of a far-off planet watching the sun set over a calm ocean, you start a stopwatch just as the top of the sun disappears. you then stand, elevating your eyes by a height h = 1.63 m, and stop the watch when the top of the sun again disappears. if the elapsed time is t = 10.1 s, what is the radius r of the planet to two significant figures? notice that duration of a solar day at the far-off planet is the same that is on earth. (hint: see sample problem 1-4.)

Answer 1

The solution for this problem is:

In 10.1 seconds the earth rotates by 10.1 /(24*60*60)*360 deg = 0.04208333 deg 

In that time a triangle has been created with the 2 longer sides having lengths r and r+1.95 

Cos (0.04208) = r/(r+1.95) 
= 0.999

r(1-0.999) =1.95*0.999 
r = 1948.05m