This looks almost identical to the one I answered here
http://www.jiskha.com/display.cgi?id=1359417542
For a boat to float in a tidal bay, the water must be at least 2.7 meters deep. The depth of the water around the boat, d(t), in meters, where t is measured in hours since midnight, is d(t) = 5 + 4.6 sin(0.5t).
(a) What is the period of the tides in hours? (Round your answer to three decimal places.)
I think it is 12.566 hrs.
The period is 2pi/B so 2pi/0.5 which equals 12.566
b) If the boat leaves the bay at midday, what is the earliest time it can return before the water becomes too shallow? (Round your answer to the nearest minute.)
I just don't know how to even start solving this question.
I think maybe this is how you do it? Please correct me!
Is it:
2.7 = 5 + 4.6 sin(0.5t)
(subtract 5 from both sides)
-2.3 = 4.6sin(0.5t)
(divide by 4.6 from both sides)
-0.5=sin(0.5t)
arcsin(-0.5) = 0.5t
Then when I plug the arcsin into my calculator I get -30 which doesn't seem right at all.
Thank you so much for all your help!
2 answers
Thank you so much!! That really helped!