Math

The average depth of the water at the end of the dock is 6 feet. High tide occurs at 6 am and low tide occurs at 6 pm. The depth of the water at high tide is 9 feet. The information can be graphed using a sinusoidal function. Your boat needs at least 4.5 feet of water to come into the dock. What times of the day is the water going to be too low to come into the dock?

  1. 👍
  2. 👎
  3. 👁
  1. model this as depth of water:
    D=6 -3sin wt w=PI/12 and t is in Universal 24 hr time (6am is 6, 6PM is 18)

    so when is D<4.5
    4.5=6-3sin(PI*t/12)
    sin(PI*t/12)=1/2
    PI*t/12=(30 deg)=PI*t/6
    t=2, so by symettry, at low tide +- 2hrs, the boat wont float. That is 4Pm to 8PM

    1. 👍
    2. 👎
    👤
    bobpursley
  2. Wow thank you so much :)

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. word problems

    In certain deep parts of oceans, the pressure of sea water, in pounds per square foot, at a depth of d feet below the surface, is given by P=16+7d/11 If a scientific team uses special equipment to measures the pressure under water

  2. calculus

    A conical water tank with vertex down has a radius of 12 feet at the top and is 23 feet high. If water flows into the tank at a rate of 20 {\rm ft}^3{\rm /min}, how fast is the depth of the water increasing when the water is 17

  3. Math

    A swimming pool is 40 feet long, 20 feet wide, 8 feet deep at the deep end, and 3 feet deep at the shallow end; the bottom is rectangular. If the pool is filled by pumping water into it at the rate of 40 cubic feet per minute, how

  4. math please help!!

    The depth d of water in a tank oscillates sinusoidally once every 4 hours. If the smallest depth is 7.9 feet and the largest depth is 10.1 feet, find a possible formula for the depth in terms of time t in hours. (Let the water

  1. Maths

    May someone help me with this HW problem? The depth (D metres) of water in a harbour at a time (t hours) after midnight on a particular day can be modelled by the function D = 2 sin(0.51t - 0.4) +5, t

  2. Physics

    A high diver of mass 65.0 kg steps off a board 10.0 m above the water and falls vertical to the water, starting from rest. If her downward motion is stopped 2.30 s after her feet first touch the water, what average upward force

  3. math

    A conical water tank with vertex down has a radius of 13 feet at the top and is 28 feet high. If water flows into the tank at a rate of 10 {\rm ft}^3{\rm /min}, how fast is the depth of the water increasing when the water is 17

  4. Math

    Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a constant rate of 3 cubic feet per minute. If the pool has radius 6 feet and height 10 feet, what is the rate of change of the height

  1. Math

    A conical water tank with vertex down has a radius of 10 feet at the top and is 22 feet high. If water flows into the tank at a rate of 30 {\rm ft}^3{\rm /min}, how fast is the depth of the water increasing when the water is 14

  2. calculus

    A conical water tank with vertex down has a radius of 12 feet at the top and is 28 feet high. If water flows into the tank at a rate of 30 ft^3/min, how fast is the depth of the water increasing when the water is 16 feet deep?

  3. Trig

    The depth of water in a tank oscilliates sinusoidally once every 6 hours. If the smallest depth is 5.5 feet and the largest depth is 8.5 feet, find a possible formula for the depth of time inhours. I say f(x)=6.75+1.25sin(pi/3) Am

  4. cal

    A conical tank (with vertex down) is 12 feet across the top and 18 feet deep. If water is flowing into the tank at a rate of 18 cubic feet per minute, find the rate of change of the depth of the water when the water is 10 feet

You can view more similar questions or ask a new question.