dafidav said:
if you wrote 4.28am then isnt that for the earliest time for the ship to leave??
it asked for the lastest time...
Heres the working for it:
You dont really need i or ii for it, just the cos bit.
Let 4(pi)t/25 = X
High tide - Low tide = 6m (given)
Hence Amplitude = 3
water must be at least 2m above low ( 1 below equilibrium)
hence
-1=3cosX
X=arccos(-1/3)
4pi x t/25 = arccos(-1/3)
t = 25arccos(-1/3) / 4pi
t = 3 Hr 48 min
but, tides occur 1 hour earlier than the wharf, so t-1 = 2Hr 48 min after high tide @ 2a.m. (wharf)
so due to the nature of the Cosine curve, the first answer is the earliest (and the 7am condition), so ship needs to be at the habour entrance by 2am + 2.48 = 4.48.
20 minute trip from wharf to habour, so latest time = 4.48 - .20 = 4.28am
It can only leave between 4.05am and 4.28am, hence 4.28 is latest