Physics, 25.12.2019 02:31, Slytherinsarethebest

Suppose the high tide in seattle occurs at 1: 00 a. m. and 1: 00 p. m. at which time the water is 16 feet above the height of low tide. low tides occur 6 hours after high tides. suppose there are two high tides and two low tides every day and the height of the tide varies sinusoidally.

(a) find a formula for the function y = h(t) that computes the height of the tide above low tide at time t, where t indicates the number of hours after midnight. (in other words, y = 0 corresponds to low tide.)

h(t) =

(b) what is the tide height at 11: 00 a. m.?

ft

Answers: 3

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Answers

answered: myaj580

(a)

$\displaystyle h(t)=y(t)=8\left [ 1+sin\left ( \frac{\pi}{6}t+\frac{\pi}{3} \right ) \right ]$

(b) Height at 11:00 a.m. = 12 feet

Explanation:

Sinusoidal Function

It refers to a mathematical curve with a smooth and periodic oscillation. Its name comes from the sine function but it can be a cosine function too. They only differ by the phase angle of 90 degrees or $\pi/2$ radians.

The sine function is characterized by

The minimum value is -1 when the argument is $3\pi/2$ radians or 270 degrees

The maximum value is 1 when the argument is $\pi/2$ or 90 degrees

It completes a full cycle in $2\pi$ radians (or 360 degrees)

It's zero at 0 and $\pi$

It repeats itself along infinite cycles with the same characteristics

We need to model the height of the tide above low tide at time t, t expressed in hours from midnight

We know the following data

At 1:00 and 13:00, the tide is high at 16 feet above the low tide, assumed to be 0 m

At 7:00 and 19:00, the tide is low at 0 m.

(a) The general sine function is expressed as

$y(t)=Asin(wt+\phi)+B\ \ .........[1]$

Where A is the amplitude, w is the angular frequency, $\phi$ is the phase, B is the vertical shift

We know that at t=1, the sine must be at max (value =1) and at t=7 it must be at min (value=-1). Replacing in [1]

y(1)=A(1)+B=A+B=16

y(7)=A(-1)+B=A-B=0

We get these equations

A+B=16

A=B

$Solving, A=8,\ B=8$

Using the same data as before, when t=1 the argument of the sine must be $\pi/2$ , so it reaches it max, and when t=7, the argument must be $3\pi/2$ . Then:

$w+\phi=\pi/2$

$7w+\phi=3\pi/2$

Solving, we get

$w=\pi/6$

$\phi=\pi/3$

The function is complete now

$\displaystyle y(t)=8sin\left ( \frac{\pi}{6}t+\frac{\pi}{3} \right )+8$

Factoring

$\displaystyle h(t)=y(t)=8\left [ 1+sin\left ( \frac{\pi}{6}t+\frac{\pi}{3} \right ) \right ]$

(b) We need to find h when t=11

$\displaystyle h(11)=8\left [ 1+sin\left ( \frac{\pi}{6}11+\frac{\pi}{3} \right ) \right ]$

$\displaystyle h(11)=8\left [ 1+sin\left ( \frac{13\pi}{6} \right ) \right ]$

$h(11)=8\left (1+0.5 \right)$

$h(11)=12\ feet$

answered: Guest

think its the third option

answered: Guest

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the shielding can reduce the coupling of radio waves, electromagnetic fields and electrostatic fields. a conductive enclosure used to block electrostatic fields is also known as a faraday cage. the amount of reduction depends very much upon the material used, its thickness, the size of the shielded volume and the frequency of the fields of interest and the size, shape and orientation of apertures in a shield to an incident electromagnetic

from wikipedia

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Suppose the high tide in seattle occurs at 1: 00 a. m. and 1: 00 p. m. at which time the water is 16...