Question

1. You are on the beach in Wasaga Beach, Ontario. At 2:00 PM on June 15th, the tide is high. At that time you find that the depth at the end of the pier is 1.5 meters. At 8:00 pm the same day, the tide is low, and you find that the depth of the water is 1.1 meters. Assuming the depth of the water varies sinusoidally with time: a) Identify the key features of the sinusoidal function, and use them to sketch a graph showing two tide cycles. b) Determine an equation to represent the tide in Wasaga Beach. c) Determine the height of the water at 11:00 PM the same day. I d) Determine the first two times after high tide where the height of the water is 1.2 metres.

Answer 1

Y- Sima. Io a periodie function with beridd 271 Il center their Yo. In the foroblem we take we take the xaxis as time to counted from 2:pm de at 11pm f=q and so on. Take the Yanis to be the height hCt): A tide cycle consents of a light tide ands ist's conge- -cutive low tide. ah (2015) 105 hct) 69,1:3) 3 6 q 12 t 11 21 2pm'5 "8bm Pm Zam

a) depth at lighticle = 1.5 meter depth at low ticle lol meter Amplitude A = height from the bare line 1.5 -101 0-2 2 Period = time difference of two lighticles = 12 hours perod 220 => B = 212 (when it is low Hicle) the height of lowest Toomt is lolo (when it is high tiche) height of highest point is 7.5. height of the center the = 6 1.3.6D) Drawing the graph with time in hows starting from 2pm. The graph in stifted 3 hours to the left from its original. fooniliton. C= 3 We have light h= A sin sin (304+c)) + is the equation in h= 0.23in (2.946 +3 + D 3 ) +1.3 1.3 meters © at llom tine cefferona from 2pm = 9 hours right = h (3) - 02 sin((918)) +13 @ Given h=12 Carmen (+ +3)) +13 sinci 2 C++3)) - -Ź -(+13) 71 >> += (7-3), (11-3) =4,8 2 6pm, 10 bm 1.2 - 02 sin 271 12 = 70 - 11 TI 6

+ 10 x 0.2 sin( (s + 3)-1.30 <<< 24 y = 1.2 x -10 10 (0, 1.5) (6, 1.1) (9.1.3) (4,1.2) (8.1.2) 1-100 8 119 10 11 12. 13 14 15 16 17 18 19 20 21 22 23 24