Homework SourseWhen satellites observe the Earth they can scan only part of
When satellites observe the Earth, they can scan only part of theEarth\'s surface. Some satellites have sensors that can measure theangle ? shown in the figure. Let hrepresent the satellite\'s distance from the Earth\'s surface and letr represent Earth\'s radius.
Find the rate at which h is changing with respect to? when ? = 30
Find the rate at which h is changing with respect to? when ? = 30
Solution
imagine a circle From centre of earth(O) the satellite is at a distance r+h (A) From centre to the point on earth up to the point where satellite can scan the distance is r (radius of earth) (point B) in triangle OAB angle B is 90 OA = r+h OB = r angle OAB = ? sin (?) = opp side /hyp = r/(r+h) csc (?) = (r+h)/r csc (?) = 1 + h/r csc( ?) - 1 = h/r h = r(csc( ?) - 1 ) dh/d? = -r csc (? )cot( ?) = - 3960 csc 30 cot 30 = --13717.84
