Explanation:
Given that, the height of the tide measured at a seaside community varies according to the number of hours t after midnight. The height is given by the equation as :

When the tide first be at 6 ft, put h = 6 ft in above equation as :


On solving the above equation to find the value of t. It is equal to :
t = 3.551 seconds
or
t = 8.449 seconds
So, the tide of 6 ft is at 3.551 seconds and 8.449 seconds. Hence, this is the required solution.
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This question involves the concepts of dynamic pressure, volume flow rate, and flow speed.
It will take "5.1 hours" to fill the pool.
First, we will use the formula for the dynamic pressure to find out the flow speed of water:

where,
v = flow speed = ?
P = Dynamic Pressure = 55 psi
= 379212 Pa
= density of water = 1000 kg/m³
Therefore,

v = 27.54 m/s
Now, we will use the formula for volume flow rate of water coming from the hose to find out the time taken by the pool to be filled:

where,
t = time to fill the pool = ?
A = Area of the mouth of hose =
= 1.98 x 10⁻⁴ m²
V = Volume of the pool = (Area of pool)(depth of pool) = A(1.524 m)
V =
= 100.1 m³
Therefore,

<u>t = 18353.5 s = 305.9 min = 5.1 hours</u>
Learn more about dynamic pressure here:
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Answer:
Explanation:
Given
mass of spring 
extension in spring 
downward velocity 
Position in undamped free vibration is given by

where 
also 



it is given


substituting values we get






