Question

14) (5m) Between midnight and midday the height, h, of the tide in 1 - 3+1.3cos Shanghai Harbour is given by where h is in metres and t is in hours with t= 0 at midnight. (i) What is the value of h at low tide, and at what time does low tide occur? (ii) Xinzhuo, Bing and Isabel wish to search the bottom of the harbour for lost treasure. They can only do this when the tide is below 2.5m. Between what times are the divers able to search for the lost treasure? 打开Word

Answer 1

14 Given h = 3 + 1.3 cos nyt (i) Since OER -13 cos os 1 so the lowest possible value of his he = 3-4.3 and we have to find out those values of t's for which h = he .. 3-1:3 COS(a) COS (2n+1)*, NE 2 3 + 1.3 cws 7 cas / -1 I SE (2n+1) = 3(2n+1) NEZ 16 Fri { nEZ Since 0% [ ? 24 SO t = 3, 9, 15, 21. in the value of h at low tide is (3-73) m 1.7 m, and it occurs at 3 A.M., 9 A.M., (15-12) P.M-3p.m. and at (21-12) P.M = 9 P.M.

17 Sat (ii) According to the question findout those t for which het) <2.5 we have to < 2.5... on, 25-3 14.3 0.5 1.3. 11 5 13. te.. 3 + 1-3-cast cos at Now we solve cos at sa and it gives 좋다 cost (5) cos" (-5) Since cos It -15 cost.< 11 on t 17 5 13 13 costo 2ñ NET/ So, 7 - 5 / 5 şt+213 € (0.625665921 , 12-0.62566592 (+2n) € (0:625665926, 6-0.62586593 te (360-62566592 - 2n), 3(2-0.62566992–2n), 3 M T W T f S S 1 2 4 5 6 7 S 9 10 11 12 13 14 15 16 178 March 2007 enER nez

19 Mon 9 For n=0 > Forn 0 For nez* = {1,2, ... } {1,2,...} , t becomes negative which is not possible. We will find those t which are lying between 0 and 24 ++ (3X0-62566592 , 3 (2-0-62566 5665921) te (01-87699775., 4./2300225) For n=1); ZE 3% (0.62566592+2), 38(2-0.62566592 +2 +2) i-e.lte (7.876699 775, 10-12380225 te (34(0.62566542+4) 31(2-0-62566592+4) iete (13-87699775, 16-12300225 Similarly ZU Tue for n=43). 6€ (19.87699775 , 22.12 300225 ) For ne-4 t exceeds 24 , so we neglect them. For natal, ..2 So, between 1.8769975 AM to 4:12 300225 AM the atmost 01:52:37.2 AiM to 04:07: 22.8 AM ... T hour min see hn min from 07:52:37.2 A.M to 10:07 : 22-8 AM sec 1 4 M T W T F S S 2 3 5 í 7 8 9 10 11 12 13 14 15 16 17 18 22 23 24 25 26 27 28 29 30 31 January 2007 ... from 01:52:37.2 P.M. to .04:07 • 22.8.P.M. and from 107:52:37.2 P.mi to 10:07 : 22:8 P.M. they divers would be able to search Los6 freasure.