Time for boat to enter harbour

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In summary, the equation for the tide is y = -cos(2π/6t) + 2 and when y = 1.5 m, t = 1. However, the answer key states t = 2, which may be incorrect due to a possible error in the given information. It is likely that the textbook author intended to state that the time between successive low tides is 12 hours, not 6, resulting in a t value of 1. This discrepancy was brought to attention by DaveC426913 and supported by Doc Al and Mark44.
  • #1
songoku
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Homework Statement
Please see the picture below
Relevant Equations
Simple harmonic motion
1634178732447.png


Equation for the tide:
$$y=-\cos \left(\frac{2 \pi}{6}t\right)+2$$

When ##y## = 1.5 m :
$$1.5=-\cos \left(\frac{2 \pi}{6}t\right)+2$$
$$-0.5=-\cos \left(\frac{\pi}{3}t\right)$$
$$\frac{\pi}{3}=\frac{\pi}{3}t$$
$$t=1$$

But the answer key is t = 2. Where is my mistake?

Thanks
 
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  • #2
songoku said:
$$-0.5=-\cos \left(\frac{\pi}{3}t\right)$$
$$\frac{\pi}{3}=\frac{\pi}{3}t$$
How did you get from one line to the other? Show your work.
 
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  • #3
DaveC426913 said:
How did you get from one line to the other? Show your work.
$$-0.5=-\cos \left(\frac{\pi}{3}t \right)$$
$$\cos^{-1} (0.5)=\frac{\pi}{3}t$$
$$\frac{\pi}{3}=\frac{\pi}{3}t$$
 
  • #4
Hm.
Ballparking suggests the textbook answer may be wrong.

1634183452163.png


But don't take my word for it; I'm just spit-balling, to jog your thought process.
 
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  • #5
Thank you very much DaveC426913
 
  • #6
I agree with your result (and with @DaveC426913). What textbook is this from?
 
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  • #7
I suspect that the textbook author meant to write: the time between successive low tides is 12 hours (not 6).

After all, there should be about two tides per day (in most places), not four! :-p
 
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  • #8
Doc Al said:
I suspect that the textbook author meant to write: the time between successive low tides is 12 hours
I think you're right.
 
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  • #9
Doc Al said:
I agree with your result (and with @DaveC426913). What textbook is this from?
This is question given by teacher

Thank you very much Doc Al and Mark44
 
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Related to Time for boat to enter harbour

What factors affect the time it takes for a boat to enter a harbour?

The time it takes for a boat to enter a harbour can be affected by several factors, such as the size and speed of the boat, the weather conditions, the presence of other boats or obstacles in the harbour, and the skill of the boat's captain.

How can the time for a boat to enter a harbour be calculated?

The time for a boat to enter a harbour can be calculated by dividing the distance from the entrance of the harbour to the dock by the speed of the boat. This will give you an estimated time, but it may vary depending on the factors mentioned above.

What is the average time it takes for a boat to enter a harbour?

The average time for a boat to enter a harbour can vary greatly depending on the factors mentioned above. However, on average, it can take anywhere from 5-15 minutes for a boat to enter a harbour.

Can the time for a boat to enter a harbour be affected by tides?

Yes, tides can greatly affect the time it takes for a boat to enter a harbour. If the tide is low, the boat may need to navigate through shallower waters, which can slow down its speed and therefore increase the time it takes to enter the harbour.

Is there a specific time of day that is best for a boat to enter a harbour?

The best time for a boat to enter a harbour may vary depending on the specific harbour and its location. However, in general, it is best to enter a harbour during daylight hours when visibility is better and the weather conditions are typically more favorable.

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