3)
check the picture below.
bearing in mind that the point of tangency, the green one there, is always a right-angle, then we get that much for the distance AB.
since the satellite can emit a signal at a speed of 186,000 miles/second, how long will it be to cover AB? well, it'll just be AB/186000, which is about 0.1381 seconds.
and how long will it be to cover the distance AE? well, it'll just be AE/186000, which is about 0.11828 seconds.
of course is quicker to AE since it's closer, so the difference for both distances will be AB - AE, which is about 0.01984121052328095721 seconds.
4)
if the satellite makes a revolution, or 2π, in 24 hours, and we know the satallite is orbiting at 22000+4000 or 26000 miles from the center of the Earth, thus its circular orbit has a radius of 26000, how many miles is that?
well, Circumference of a circle is C = 2πr, if r = 26000, then C = 2π(26000), so on those 24 hours it has covered 52000π miles.
how fast must it travel then? [tex]\bf \cfrac{52000\pi }{24}~\cfrac{miles}{hours}\qquad \approx \qquad 6806.78~\frac{miles}{hour}[/tex]
now if you need the rate in miles/seconds, bear in mind that an hour has 60 minutes and each minute 60 seconds, thus and hour has 60*60 seconds or 3600, thus its speed in miles/seconds will be 52000π/3600.
