SOLUTION: problem solving question the depth of water d meters, at a port entrance is given by the function d(t) = 4.5 + 1.5 sin pi t/12 where t is hours a certain ship needs the

Question 1029598: problem solving question
the depth of water d meters, at a port entrance is given by the function
d(t) = 4.5 + 1.5 sin pi t/12
where t is hours
a certain ship needs the depth at the port entrance to be more than 5 meters. The ship can be loaded and unloaded in and out of the port in 9 hours. assuming the the ship enters the port just as the depth at the entrance passes 5 meters, will the ship be able to exit 9 hours later? How long will it have to spare? or by how many minutes will it miss out?

and can you please show me working out and how you got the answer.
Thankyou
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
d(t) = 4.5 + 1.5 sin pi t/12
:
5 = 4.5 + (1.5 * sin(pi * t/12))
:
0.5 = 1.5 * sin(pi * t/12)
:
note that pi = 180 degrees
:
1/3 = sin(15t)
:
determine angle from inverse sin function = 1/3
:
15t = 19.471220634
:
*********************************
t = 1.298081376 approx 1.3 hours
*********************************
:
we need 9 hours to unload the ship
:
d(10.3) = 4.5 + (1.5 * sin(pi * (10.3)/12)) =
:
4.5 + (1.5 * 0.430511097) = 5.145766646 meters
:
****************************************************************
*****yes, the ship will be able to exit 9 hours later
:
the sin curve is periodic, here is a graph of the equation
:

:
we want to know the value of t when the sin(15t) = 1/3 again *****
:
note we subtract 19.471220634 from 180 = 160.528779366
:
15t = 160.528779366
:
t = 10.701918624
:
***The ship has an addition 24 minutes before it can not sale out of the harbor
:
RELATED QUESTIONS
At an ocean port on a certain day, the water has a depth of d metres at a time t hours... (answered by Alan3354)

The water level at an ocean inlet has a depth, d in meters, that varies with the time, t, (answered by ikleyn)

the height of the water H in feet at a boat dock t hours after 6 a.m. is given by... (answered by Alan3354,rothauserc)

The water at a local beach has an average depth of one meter at low tide and an average... (answered by robertb)

the height of the water H in feet at a boat dock t hours after 6 a.m. is given by... (answered by Alan3354)

1) A rectangular enclosure,subdivided into 3 congruent pens,is to be made using a barn as (answered by stanbon)

In a particular harbour, high tide occurred at midnight. The depth of the water in a... (answered by Theo)

for a certain day the depth of water,h, in metres in Tofino,B.C at time t, in hours, is... (answered by addingup)