- #1
Karol
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Homework Statement
In a port the tide and the low tide change with harmonic motion. at the high tide the water level is 12 meters and at the low tide it is 2 meters. between the tide and the low tide there are 6 hours.
A ship needs 8 meters of water depth. how long can it stay in the port
Homework Equations
Harmonic motion: $$x=A\cos(\omega t)$$
The period: $$T=\frac{2\pi}{\omega}$$
The Attempt at a Solution
The difference in depth between tide and low tide is 10 meters, so the middle point, the 0 point is at 7 meters. the ship can stay until the water reaches water level of 8 meters which is 1 meter above the 0 level.
##T=\frac{2\pi}{\omega}\rightarrow 12\times 3600=\frac{2\pi}{\omega}\Rightarrow \omega=0.000145##
##x=A\cos(\omega t)\rightarrow 1=5 \cos(0.000145\cdot t)\Rightarrow 0.000145\cdot t=78.5^0##
##\rightarrow 1.37[rad]=0.000145\cdot t \Rightarrow t=9444[sec]=2.6[hour]##
It should be 5.2 hours, although i can't understand why since it is almost the time between tide and low tide and we need a point above the 0 point
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