SOLUTION: The water at a local beach has an average depth of one meter at low tide and an average depth at high tide of 8m. One cycle of the tides takes approximately 12 hours. This periodic

Question 1183639: The water at a local beach has an average depth of one meter at low tide and an average depth at high tide of 8m. One cycle of the tides takes approximately 12 hours. This periodic motion can be modelled by the function
d(t)=3.5 cos [(pi/6)t]+4.5 where d(t) represents the depth of the water, in metres, at a time t, in hours. This equation assumes that the water level is at high tide at time zero (midnight). Many people dive into the water from a nearby dock. If the water must be at least 3m deep to dive safely, when during the first 24 hour period (in hours) would it be safe to dive off the dock? Please give your answer in all ranges of hours possible.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
The periodic motion is modelled by
, where t = 0 starts at midnight.
We want to find the values of t where .

===>

===> ===>

===> ~ 3.85 hours after midnight.

The ranges of time where it is safe to dive, i.e., , are then
[0, 3.85], [8.15, 15.85], and [21.85, 24].

These correspond to the following times when it is safe to dive:
12:00 am - 3.51 am, 8:09 am - 3:51 pm, and 9:51 pm - 12:00 am.

RELATED QUESTIONS
the water at a local beach has an average depth of one meter at low tide and an average... (answered by greenestamps)

1.The water at a local beach has an average depth of 1 metre at low tide. The average... (answered by stanbon)

12. The nearby beach has an average depth of the water at low tide of 1 m at midnight.... (answered by Theo,ikleyn)

The average depth of water at the end of a dock is 7 feet. This varies 3 feet in both... (answered by ikleyn)

The tide on a certain shore on a planet has a period of 36.5 hours, and the high tide... (answered by josmiceli,Alan3354,jim_thompson5910)

Can somebody please help me out with this?? Coastal areas experience tides which is... (answered by Theo)

In Crescent Moon Bay in July, high tide is at 3:00 pm. The water level is 6 feet at high... (answered by josmiceli)

In Crescent Moon Bay in July, high tide is at 3:00 pm. The water level is 6 feet at high... (answered by ikleyn)

The water level varies from 12 inches at low tide to 52 inches at high tide. Low tide... (answered by yahkay)