Time for boat to enter harbour

[songoku]

Homework Statement

Please see the picture below

Relevant Equations

Simple harmonic motion

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

 

[DaveC426913]

$$-0.5=-\cos \left(\frac{\pi}{3}t\right)$$
$$\frac{\pi}{3}=\frac{\pi}{3}t$$

How did you get from one line to the other? Show your work.

 

[songoku]

How did you get from one line to the other? Show your work.

$$-0.5=-\cos \left(\frac{\pi}{3}t \right)$$
$$\cos^{-1} (0.5)=\frac{\pi}{3}t$$
$$\frac{\pi}{3}=\frac{\pi}{3}t$$

 

[DaveC426913]

Hm.
Ballparking suggests the textbook answer may be wrong.

But don't take my word for it; I'm just spit-balling, to jog your thought process.

 

[songoku]

Thank you very much DaveC426913

 

[Doc Al]

I agree with your result (and with @DaveC426913). What textbook is this from?

 

[Doc Al]

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!

 

[Mark44]

I suspect that the textbook author meant to write: the time between successive low tides is 12 hours

I think you're right.

 

[songoku]

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