Can a Ship Enter a Harbor? Calculating Depth Using h(t) = 3 + 2sin(0.5236t)

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The discussion revolves around determining the time a ship can safely enter a harbor based on the depth function h(t) = 3 + 2sin(0.5236t), where the minimum required depth is 4.5 meters. Participants are trying to solve for the values of t when h(t) meets or exceeds this depth. A user initially calculated sine solutions but struggled to find the correct time interval. Another participant advised correcting the calculations and suggested providing detailed steps in future attempts. The conversation emphasizes the importance of clarity and thoroughness in mathematical problem-solving.
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Homework Statement


h(t) = 3 + 2sin(0.5236t)
h = depth in meters (water)
t = number of hours after 7

1) A certain ship can only enter the harbor if the depth is 4.5m or more. For how long can this ship stay at the harbor?

Homework Equations

The Attempt at a Solution


I tried getting both of the sine solutions 1.619 and 2.293. I substracted the former from the latter but that didn't work. Can anyone point me in the right direction?
 
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BadatPhysicsguy said:

Homework Statement


h(t) = 3 + 2sin(0.5236t)
h = depth in meters (water)
t = number of hours after 7

1) A certain ship can only enter the harbor if the depth is 4.5m or more. For how long can this ship stay at the harbor?

Homework Equations

The Attempt at a Solution


I tried getting both of the sine solutions 1.619 and 2.293. I substracted the former from the latter but that didn't work. Can anyone point me in the right direction?
You forgot to divide 2.293 with 0.5236.
 
Write out your solution in full detail next time, to show how much work you have done. :)
 

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