Math

Ok, I'm lost on this....

The equation D=1.2 gives the distance, D in miles that a person can see to the horizon from a height h in feet. Solve this equation for h

  1. 👍 0
  2. 👎 0
  3. 👁 221
  1. You left out information in your equation. The equation I find for this is D=sqrt(13h). The equation in your book may be differnt.

    Solve for h
    D^2=13h
    h=(D^2)/13

    1. 👍 0
    2. 👎 0
  2. A question that often arises amongst cruise passengers is how high a building can be seen from a ship at sea? A similar reverse question is how far can one see from the top of a building? An easy way to rephrase the question is to ask what is the distance from the top of a skyscraper to the horizon? Lets see if we can create a picture of the problem.

    Draw yourself as large a circle as possible on a sheet of paper. Label the center O. Draw a vertical line from O to point A on the upper circumference. Extend the line past the circumference slightly to point B. Draw another line from O, upward to the right at an angle of ~30º to the vertical line, and intersecting the circumference at point C, our horizon point. Label OA and OC as r, the radius of the Earth. Label AB as h, the height of our make believe building. Label BC as d, the distance from the top of the building to the horizon or a ship at sea. Angle OCB = 90º.

    From the Pythagorean Theorem, we can write that d^2 + r^2 = (r + h)^2 = r^2 + 2rh + h^2.
    Simplifying, we get d^2 = 2rh + h^2 or d = sqrt[h(2r + h)].
    The mean radius of the Earth is 3963 miles which is 20,924,640 feet.
    Therefore, our distance d becomes d = sqrt[h(41,849,280 + h)].
    If we wish to determine how far we can see from a building 1000 feet high, we need only compute d = sqrt[1000(41,849,280 + 1000)] = 204,573 feet or 38.7448 miles, ~38.74 miles.

    If we were interested in determining how high a building we could see from a distance at sea, we need only solve our expression above for h which must make use of the quadratic formula. Rearranging our expression to h^2 + 2rh - d^2 = 0, we find that h = [-2r+/-sqrt(4r^2 + 4d^2)]/2 which simplifies to h = sqrt(r^2 + d^2) - r. Using our distance of ~38.75 miles calculated above, we can now solve for h = sqrt(20,924,640^2 + (38.75(5280)) - 20,924,640 which turns out to be 1000 feet.

    Our expression for d can actually be simplifed somewhat due to the insignificance of h relative to r. We can easily rewrite the expression as d = sqrt(2rh) and not lose any accuracy to speak of. Taking it a step further, and since it is convenient to use h in feet, we can write d = sqrt[2(3963)miles(h)miles] = sqrt[1.5h].
    ...........................................................5280 ft.
    Using our 1000 foot high building again with the simplified expression, we get d = sqrt[1.5(1000)] = 38.7298 miles or ~38.73 miles, or approximately 79 feet difference.

    For D = sqrt(1.5h), D^2 = 1.5h making h = D^2/h, h in feet, D in miles.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    find the constant of proportionality and unit rate for the data in the table. Then write the equation to represent the relationship between time t and distance d Time Distance 2 hrs 90 miles 3 hrs 135 miles 5 hrs 225 miles 6 hrs

  2. math

    The equation d =70t represents the distance in miles covered after traveling at 70 miles per hour for t hours.....what is d when t = 2.5? ...what is t when d =210? please help im desperate here...iv been studying all day help me

  3. math

    A lawyer drives from her home, located 6 miles east and 10 miles north of the town courthouse, to her office, located 4 miles west and 14 miles south of the courthouse. Find the distance between the lawyer's home and her office. I

  4. math

    on a drive through allegheny county,natalie drove due west for 9 miles,then turned left and proceeded to drive due south.after traveling 12 miles south,what was the straight 12 miles line distance between where natalie startd and

  1. Algebra

    A car can average 140 miles on 5 gallons of gasoline. Write an equation for the distance "d" in miles the car can tavel on "g" gallons of gas?

  2. 3 questions Math

    18. What is the simpler form of the following expression? (6x^3 - 1x +1) divided by (2x + 1) -3x^2 + 2x - 1 3x^2 - 2x + 1 -3x^2 + 2x - 1 3x^3 + 2x - 1 19. Solve the equation. 1/2x + 14 - 9/x + 7 = -6 x = - 101/12 x = 101/12 x = -

  3. math

    last week, Mr thomas rode his bike 49 miles. this week mr. Thomas rode 14 miles less than he did last week.Mr thomas rode the same distance each of the 7 days this week. write an equation to find the number of miles,m, he rode

  4. Physics

    A 70.0 kg base runner begins his slide into second base while moving at a speed of 4.0 m/s. The coefficient of friction between his clothes and Earth is .70. He slides so that his speed is zero just as he reaches the base. How

  1. pre-algebra

    your family is driving to houston,texas.A sign indicates that you are 700 miles from houston.Your car's trip odometer indicates you are 400 miles from home.YOu are traveling at an average speed of 60 miles per hour. A. write an

  2. math

    your family is driving to houston,texas.A sign indicates that you are 700 miles from houston.Your car's trip odometer indicates you are 400 miles from home.YOu are traveling at an average speed of 60 miles per hour. A. write an

  3. Reading

    Establish a Running Plan A 5-kilometer race is a little over 3 miles long. It is best to start by running a shorter distance and then gradually increase your running distance. This chart will help you to establish a running plan

  4. physics

    Suppose that the displacement of a particle is related to time according to the expression delta x = ct^3. What are the SI units of the proportionality constant c? My answer: delta x = ct^3 m = c s^3 (s: seconds) m/s^3= c The SI

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