<span>f(x) = 5.05*sin(x*pi/12) + 5.15
First, you need to determine the period of the function. The period will be the time interval between identical points on the sinusoidal function. For this problem, the tide is rising and at 5.15 at midnight for two consecutive days. So the period is 24 hours. Over that 24 hour period, we want the parameter passed to sine to range from 0 to 2*pi. So the scale factor for x will be 2*pi/24 = pi/12 which is approximately 0.261799388. The next thing to note is the magnitude of the wave. That will simply be the difference between the maximum and minimum values. So 10.2 ft - 0.1 ft = 10.1 ft. And since the value of sine ranges from -1 to 1, we need to divide that magnitude by 2, so 10.1 ft / 2 = 5.05 ft.
So our function at this point looks like
f(x) = 5.05*sin(x*pi/12)
But the above function ranges in value from -5.05 to 5.05. So we need to add a bias to it in order to make the low value equal to 0.1. So 0.1 = X - 5.05, 0.1 + 5.05 = X, 5.15 = X. So our function now looks like:
f(x) = 5.05*sin(x*pi/12) + 5.15
The final thing that might have been needed would have been a phase correction. With this problem, we don't need a phase correction since at X = 0 (midnight), the value of X*pi/12 = 0, and the sine of 0 is 0, so the value of the equation is 5.15 which matches the given value of 5.15. But if the problem had been slightly different and the height of the tide at midnight has been something like 7 feet, then we would have had to calculate a phase shift value for the function and add that constant to the parameter being passed into sine, making the function look like:
f(x) = 5.05*sin(x*pi/12 + C) + 5.15
where
C = Phase correction offset.
But we don't need it for this problem, so the answer is:
f(x) = 5.05*sin(x*pi/12) + 5.15
Note: The above solution assumes that angles are being measured in radians. If you're using degrees, then instead of multiplying x by 2*pi/24 = pi/12, you need to multiply by 360/24 = 15 instead, giving f(x) = 5.05*sin(x*15) + 5.15</span>
Answer:
4500 J
Explanation:
First, let's define some equations and derivations.
Our potential energy formula is:
Where <em>m </em>is mass (in kg), <em>g</em> is the gravitational constant (in m/s²), and <em>h</em> is height (in m).
We also know that <em>mg</em> is equal to the weight of an object (in N), from Newton's 2nd Law of Motion: F = ma (Force is equal to [constant] mass times acceleration).
Therefore, we can simply substitute force into the equation:
Where <em>F</em> is the force (in N) and <em>h</em> is still height (in m).
Now we can calculate the amount of potential energy in our system, measured in joules.
Substitute in the given variables, F = 500 N and h = 9 m:
Using simple Pre-Algebra rules, we find that:
This tells us that the we have 4500 joules of potential energy when I am 9 meters above the water on the edge of the diving board.
Answer:
Given
initial velocity (u) =27.030
Force of gravidity g) =9.8
Rtc maximum height Hmix =?
Answer:Broadly speaking, all energy in the universe can be categorized as either potential energy or kinetic energy. Potential energy is the energy associated with position, like a ball held up in the air. When you let go of that ball and let it fall, the potential energy converts into kinetic energy, or the energy associated with motion.
EXAMPLES: There are five types of kinetic energy: radiant, thermal, sound, electrical and mechanical. Let's explore several kinetic energy examples to better illustrate these various forms.
