1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
PilotLPTM [1.2K]
3 years ago
10

Some of the highest tides in the world occur in the Bay of Fundy on the Atlantic Coast of Canada. At Hopewell Cape the water dep

th at low tide is about 2.0 m and at high tide it is about 12.0 m. The natural period of oscillation is a little more than 12 hours and on June 30, 2009, high tide occurred at 6:45 AM. This helps explain the following model for the water depth D (in meters) as a function of the time t (in hours after midnight) on that day: D(t) = 7 + 5 cos[0.503(t − 6.75)]. How fast was the tide rising (or falling) at the following times? (Round your answers to two decimal places.) (a) 5:00 AM m/h (b) 6:00 AM m/h (c) 7:00 AM m/h (d) Noon m/h
Physics
1 answer:
Nady [450]3 years ago
4 0

Answer:

(a) 1.939 m/h

(b) 0.926 m/h

(c) -0.315 m/h

(d) -1.21 m/h

Explanation:

Here, we have the water depth given by the function of time;

D(t) = 7 + 5·cos[0.503(t-6.75)]

Therefore, to find the velocity of the depth displacement with time, we differentiate the given expression with respect to time as follows;

D'(t) = \frac{d(7 + 5\cdot cos[0.503(t-6.75)])}{dt}

= 5×(-sin(0.503(t-6.75))×0.503

= -2.515×(-sin(0.503(t-6.75))

= -2.515×(-sin(0.503×t-3.395))

Therefore we have;

(a) at 5:00 AM = 5 -  0:00 = 5

D'(5) =  -2.515×(-sin(0.503×5-3.395)) = 1.939 m/h

(b) at 6:00 AM = 6 -  0:00 = 6

D'(5) =  -2.515×(-sin(0.503×6-3.395)) = 0.926 m/h

(c) at 7:00 AM = 7 -  0:00 = 7

D'(5) =  -2.515×(-sin(0.503×7-3.395)) = -0.315 m/h

(d) at Noon 12:00 PM = 12 -  0:00 = 12

D'(5) =  -2.515×(-sin(0.503×12-3.395)) = -1.21 m/h.

You might be interested in
Starting from rest, a disk rotates about its central axis with constant angular acceleration. in 6.00 s, it rotates 44.5 rad. du
Klio2033 [76]

a. The disk starts at rest, so its angular displacement at time t is

\theta=\dfrac\alpha2t^2

It rotates 44.5 rad in this time, so we have

44.5\,\mathrm{rad}=\dfrac\alpha2(6.00\,\mathrm s)^2\implies\alpha=2.47\dfrac{\rm rad}{\mathrm s^2}

b. Since acceleration is constant, the average angular velocity is

\omega_{\rm avg}=\dfrac{\omega_f+\omega_i}2=\dfrac{\omega_f}2

where \omega_f is the angular velocity achieved after 6.00 s. The velocity of the disk at time t is

\omega=\alpha t

so we have

\omega_f=\left(2.47\dfrac{\rm rad}{\mathrm s^2}\right)(6.00\,\mathrm s)=14.8\dfrac{\rm rad}{\rm s}

making the average velocity

\omega_{\rm avg}=\dfrac{14.8\frac{\rm rad}{\rm s}}2=7.42\dfrac{\rm rad}{\rm s}

Another way to find the average velocity is to compute it directly via

\omega_{\rm avg}=\dfrac{\Delta\theta}{\Delta t}=\dfrac{44.5\,\rm rad}{6.00\,\rm s}=7.42\dfrac{\rm rad}{\rm s}

c. We already found this using the first method in part (b),

\omega=14.8\dfrac{\rm rad}{\rm s}

d. We already know

\theta=\dfrac\alpha2t^2

so this is just a matter of plugging in t=12.0\,\mathrm s. We get

\theta=179\,\mathrm{rad}

Or to make things slightly more interesting, we could have taken the end of the first 6.00 s interval to be the start of the next 6.00 s interval, so that

\theta=44.5\,\mathrm{rad}+\left(14.8\dfrac{\rm rad}{\rm s}\right)t+\dfrac\alpha2t^2

Then for t=6.00\,\rm s we would get the same \theta=179\,\rm rad.

7 0
3 years ago
HELP ASAP! GIVING BRAINLIEST!!!<br><br> I need the answers to 1,2,3!!
artcher [175]

1) 72/4 = 18 years

2) 72/10 = 7.2 years

3) 72/13 = 5.54 years

Explanation: With the rule of 72, you simply take 72 and divide it by whatever the rate of return (or return on investment) is.

Let me know if you have any questions.

7 0
3 years ago
The weight of a boy having a mass of 50 kg is __N.<br> ???
lakkis [162]

Answer: 490N

Explanation:

Newton is the unit for force. Force = mass x acceleration

F=N m=50kg a=9.8 (earth's acceleration of gravity)

F=50X9.8

F≈490N

8 0
3 years ago
Your new motorcycle weighs 2450 N.
Whitepunk [10]

Answer:

Explanation:

The negative only matters reallly if you are dealing with a 2d system. I could even define down as positive and up as negative. However, usually you are taught that down is negative. It really doesn't matter because a force is a force. It is only given a direction relative to another force or vector direction.

5 0
2 years ago
To qualify to run in the 2005 boston marathon, a distance of 26.2 miles, an 18-year-old woman had to have completed another mara
oksian1 [2.3K]
3 hours and 40 minutes is equivalent to 3.667 hours. If a woman must have run another marathon (of 26.2 miles) within that time, then her minimum average speed in mph can be calculated by dividing the distance by time:
26.2 miles / 3.667 hours = 7.145 miles per hour
5 0
3 years ago
Read 2 more answers
Other questions:
  • On a hot day, you sit on the edge of a pool and dip your feet into the water, causing changes to occur that are related to the p
    11·1 answer
  • Bob has a brother, jim, who has a daughter named bertha. Bertha's daughter, jennifer, has a sister named penny. which of the fol
    5·2 answers
  • How do paved parking lots and roads with concrete or asphalt affect water flow on the land?
    6·1 answer
  • An atom’s mass number equals the number of
    15·2 answers
  • Is Kepler's constant the same for moons orbiting a planet as it is for planets orbiting the sun? Why?
    11·2 answers
  • Suppose we consider the system of the three capacitors as a single "equivalent" capacitor. Given the charges of the three indivi
    6·1 answer
  • The Cosmo Clock 21 Ferris wheel in Yokohama, Japan, has a diameter of 100 m. Its name comes from its 60 arms, each of which can
    15·1 answer
  • a 1500 kg car traveling at 15 m/s to the south collides with a 4500 kg truck that is intially at rest at a spotlight. The car an
    8·2 answers
  • How does a mirage occur in a deser?explain with a labelled diagram.​
    15·2 answers
  • A cord of mass 0.65 kg is stretched between two supports 8.0 m apart. If the tension in the cord is 120 N, how long will it take
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!