You forgot to divide 2.293 with 0.5236.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?
The equation h(t) = 3 + 2sin(0.5236t) is a mathematical model used to calculate the depth of a harbor over time. The "h" represents the depth of the harbor, "t" represents time (in hours), and "sin" is the sine function. The constant 0.5236 is the conversion factor from hours to radians, and the constant 3 represents the average depth of the harbor.
This equation helps determine if a ship can enter a harbor by providing a way to calculate the depth of the harbor at any given time. If the depth is greater than the draft (the depth of the ship's hull), then the ship can safely enter the harbor without running aground.
The "sin" function in this equation represents the periodic nature of tides, which can affect the depth of a harbor. This function allows for fluctuations in the depth of the harbor over time, rather than assuming a constant depth.
To determine the maximum depth a ship can safely enter a harbor, you would need to know the draft of the ship and the maximum allowable draft for the harbor. Then, you would plug those values into the equation and solve for "t". This would give you the maximum time (in hours) that the ship could enter the harbor without running aground. You can then plug this value back into the equation to find the corresponding maximum depth.
Yes, there are limitations to using this equation. It assumes that the depth of the harbor follows a sine wave pattern, which may not always be the case. It also does not take into account other factors such as wind, currents, or storms, which can affect the depth of the harbor. Additionally, the accuracy of the equation depends on the accuracy of the input data used (such as the average depth of the harbor). Therefore, it should be used as a general guideline rather than an exact measurement.