Tide Question (1 Viewer)

[hit patel]

There is a tide. The depth of water at low tide on a day is 0.7m and the depth of water at high tide was 3.7m. If low tide at 8:55 am and high tide at 3:05 pm. find earliest time after low tide at which a boat could enter the river if it required water to be at least 6 meters deep.

 

[obliviousninja]

Hahahaha. I loved these questions.

 

[braintic]

There is a tide. The depth of water at low tide on a day is 0.7m and the depth of water at high tide was 3.7m. If low tide at 8:55 am and high tide at 3:05 pm. find earliest time after low tide at which a boat could enter the river if it required water to be at least 6 meters deep.

Great intro - 'there is a tide'!

Let t = 0 be 8:55 am.
Since you are starting at low tide, it is a -ve cos function.

Amplitude = (3.7 - 0.7)/2 = 1.5
Centre of motion = (3.7 + 0.7)/2 = 2.2

Low to high = 6.333333 hrs = half a cycle
So period = 2(6.33333) = 38/3 = (2pi)/n
n=(3pi)/19

So the equation for the height of water is:
h=2.2 - 0.7cos (3pi/19)t

Let h = 6, solve for t, then add back the 8hrs 55 min

 

[hit patel]

Thanks +1 braintic. Yep I confirmed. Luckily I was correct. The first time I did it i forgot the 2.2 then I redid and got this.