Question

Question Five (15 marks: From an observation point on a hill overlooking at lake. A survey crew sighted a moving speedboat using a theodolite. At the first point the line of sight was N60 and the telescope was depressed at an angle of 20% slope down 20 about the point O). At the second point the line of sight was S75'W and the telescope was depressed at an angle of 15 (slope down 15" about the point O). It took 20 seconds for the speedboat to move from the first point to the second. Find: 1) in what direction is the speedboat moving? 2) what is the speed of the speedboat? The scale is 1:6000, vertical and horizontal LIL WATER LEVEL

Answer 1

Solution Given that wne of sight at first point = Noow line of sight at second point = 5750w At the first point of sight: 0= 20 nom 600 600/sinzo Z coatos level .At second point of sight 108 1600 6oolsini 5° vala level oÀ = -0A Cos 3oi & OA sin 305 OB = (OB COSIs î – OBsinis ģ - AB = 58-oh

AB = fos Cosisî oB Sing) – (A COS3oi ton sin 309) on = 60A Cos6o i toa sin con OB' = - OB COS 15:+ ob Sin 180g (-oBros159 TO A Cos 30°) i + (OB sin 15-0A sin38) 1 AB = -7.200 n-14771 Î AB = 16432

je Direction of the speed boul, tan@ = 14721 . 7200 pirn = saowl speed of the speed boat = 16432/20 = 8216 unit second]