Maths problem (sinus equation)?

Question

For my maths assignment I have to answer this question that I don't get at all...
THANKS FOR ANY HELP (: (: (:

TIDE PROBLEM.

The depth of the shallowest section of the Brisbane River motuth can be described by the equation:

Depth = 12.2 + 1.5 sin (pi t/6)     ; where 't' is the time in hours after mid-tide. (Calculation must be in radians)

The USS Navy aircraft carrier, USS Enterprise, is anchored in Moreton Bay. This ship is 250 metres in length, 25 metres wide and has a totally hull depth of 26 metres. The ship can cross the river mouth at any time when it is empty, but when full it requires a depth (at the river mouth) of at least 13 metres to manoeuvre safely.

The rising mid-tide will occur at 3.00 a.m. tomorrow and the captain is anxious to unload his cargo as soon as possible after that. CALCULATE THE EARLIEST TIME ha can safely enter the river mouth when the ship is fully laden, and CALCULATE THE SPACE OF TIME that it would continue to be safe to enter that day.

(To get a solution you must provide some algebaric working.)

THANK YOU SO MUCH FOR ANY HELP!!! You'll save my assignment as I won't have a possibility anymore to ask my teacher...

(:

Ossi G · Accepted Answer

Hello Pünktchen, (why Pünktchen, from Pünktchen and Anton, by Erich Kästner?)

Set the equation of the depth = 13
the period of the equation is 2pi/(pi/6) = 12 (hours)
13 = 12.2 + 1.5sin(pi/6*t) 
0.8/1.5 = sin(pi/6*t) 
pi/6*t = sin^-1(8/15) 
pi/6*t = 0.56253  and (pi - 0.56235 = 2.579)

t1 = 0.56253*6/pi = 1.07436 h
t2 = 2.579*6/pi = 4.92563 h
and 
t3 = 1.07436 + 12 = 13.074 h
t4 = 4.92563 + 12 = 16.9256 h

the water depth is below 13 m between t1 and t2 after 3 am
and between t3 and t4 after 3 am. 
So calculate the times.

Regards

Maths problem (sinus equation)?

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