Pilot

How high is the airplane's pilot to see 0.001 of Earth's surface?

Correct result:

h =  12.782 km

Solution:

R=6378 km S1=4π⋅ R2=4⋅ 3.1416⋅ 63782≐511185932.522 km2 S=0.001⋅ S1=0.001⋅ 511185932.522≐511185.9325 km2  S=2πRv v=S/(2π⋅ R)=511185.9325/(2⋅ 3.1416⋅ 6378)=3189250=12.756 km y=R−v=6378−12.756=6365.244 km x=R2−y2=63782−6365.2442≐403.1784 km  x/y=(h+v)/x h+v=x2/y h=x2/y−v=403.17842/6365.244−12.756=6378499=12.782 kmR=6378 \ \text{km} \ \\ S_{1}=4 \pi \cdot \ R^2=4 \cdot \ 3.1416 \cdot \ 6378^2 \doteq 511185932.522 \ \text{km}^2 \ \\ S=0.001 \cdot \ S_{1}=0.001 \cdot \ 511185932.522 \doteq 511185.9325 \ \text{km}^2 \ \\ \ \\ S=2 \pi R v \ \\ v=S / (2 \pi \cdot \ R)=511185.9325 / (2 \cdot \ 3.1416 \cdot \ 6378)=\dfrac{ 3189 }{ 250 }=12.756 \ \text{km} \ \\ y=R - v=6378 - 12.756=6365.244 \ \text{km} \ \\ x=\sqrt{ R^2-y^2 }=\sqrt{ 6378^2-6365.244^2 } \doteq 403.1784 \ \text{km} \ \\ \ \\ x/y=(h+v)/x \ \\ h+v=x^2/y \ \\ h=x^2/y - v=403.1784^2/6365.244 - 12.756=\dfrac{ 6378 }{ 499 }=12.782 \ \text{km}

Try another example


Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Showing 0 comments:
avatar




Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

You need to know the following knowledge to solve this word math problem:


 
We encourage you to watch this tutorial video on this math problem: video1   video2   video3

Next similar math problems:

  • Airplane
    tu-144 Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies?
  • Tropics and polar zones
    circles_on_Earth What percentage of the Earth’s surface lies in the tropical, temperate and polar zone? Individual zones are bordered by tropics 23°27' and polar circles 66°33'
  • Spherical cap
    gulovy_odsek Place a part of the sphere on a 4.6 cm cylinder so that the surface of this section is 20 cm2. Determine the radius r of the sphere from which the spherical cap was cut.
  • Spherical cap 4
    spherical cap What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula.
  • Thunderstorm
    blesk The height of the pole before the storm is 10 m. After a storm when they come to check it they see that on the ground from the pole blows part of the column. Distance from the pole is 3 meters. At how high was the pole broken? (In fact, a rectangular tria
  • Spherical cap
    koule2 What is the surface area of a spherical cap, the base diameter 20 m, height 2 m.
  • Calculate
    equilateral_triangle2 Calculate the length of a side of the equilateral triangle with an area of 50cm2.
  • The right triangle
    rt_tr540 The right triangle ABC has a leg a = 36 cm and an area S = 540 cm2. Calculate the length of the leg b and the median t2 to side b.
  • The ladder
    rebrik The ladder touch on a wall at a height of 7.5 m. The angle of the inclination of the ladder is 76°. How far is the lower end of the ladder from the wall?
  • Equilateral triangle
    rs_triangle_1 The equilateral triangle has a 23 cm long side. Calculate its content area.
  • Isosceles trapezium
    rr_lichobeznik_2 Calculate the area of an isosceles trapezium ABCD if a = 10cm, b = 5cm, c = 4cm.
  • Median in right triangle
    rt_triangle In the rectangular triangle ABC has known the length of the legs a = 15cm and b = 36cm. Calculate the length of the median to side c (to hypotenuse).
  • A truck
    truck_11 A truck departs from a distribution center. From there, it goes 20km west, 30km north and 10km west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)?
  • If the
    tan If the tangent of an angle of a right angled triangle is 0.8. Then its longest side is. .. .
  • Triangle P2
    1right_triangle Can triangle have two right angles?
  • Triangle
    triangle_circle Calculate the area of right triangle ΔABC, if one leg is long 14 and its opposite angle is 59°.
  • Sphere cuts
    sphere_cut At what distance from the center intersects sphere with radius R = 56 plane, if the cut area and area of the main sphere circle is in ratio 1/2.