Elevation

What must be the elevation of an observer in order that he may be able to see an object on the earth 536 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.

Correct answer:

h =  22482.4 m

Step-by-step explanation:

$$\begin{gathered} R=6378.1km \\ d=536km \\ (R+h{)}^2=d^2+R^2 \\ R+h=\sqrt{d^2+R^2} \\ h=\sqrt{d^2+R^2}-R \\ h=\sqrt{536^2+6378.1^2}-6378.1 \\ h=22482.4\text{ m} \end{gathered}$$

Try another example

Related math problems and questions:

• Horizon
  The top of a lighthouse is 19 m above the sea. How far away is an object which is just "on the horizon"? [Assume the Earth is a sphere of radius 6378.1 km.]
• Felix
  Calculate how much land saw Felix Baumgartner after jump from 32 km above ground. The radius of the Earth is R = 6378 km.
• Above Earth
  To what height must a boy be raised above the earth to see one-fifth of its surface.
• Spherical cap
  From the sphere of radius 11 was truncated spherical cap. Its height is 6. What part of the volume is a spherical cap from the whole sphere?
• Sphere - parts
  Calculate the area of a spherical cap, which is part of an area with base radius ρ = 9 cm and a height v = 3.1 cm.
• Spherical cap
  The spherical cap has a base radius of 8 cm and a height of 5 cm. Calculate the radius of a sphere of which this spherical cap is cut.
• What percentage
  What percentage of the Earth’s surface is seen by an astronaut from a height of h = 350 km. Take the Earth as a sphere with the radius R = 6370 km
• Spherical cap
  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.
• Rotation of the Earth
  Calculate the circumferential speed of the Earth's surface at a latitude of 61°​​. Consider a globe with a radius of 6378 km.
• The spacecraft
  The spacecraft spotted a radar device at altitude angle alpha = 34 degrees 37 minutes and had a distance of u = 615km from Earth's observation point. Calculate the distance d of the spacecraft from Earth at the moment of observation. Earth is considered a
• Spherical cap 4
  What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula.
• A spherical segment
  The aspherical section, whose axial section has an angle of j = 120° in the center of the sphere, is part of a sphere with a radius r = 10 cm. Calculate the cut surface.
• Sphere cuts
  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.
• Moon
  We see Moon in the perspective angle 28'. Moon's radius is 1740 km at the time of the full moon. Calculate the mean distance of the Moon from the Earth.
• Airplane
  Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies?
• Cube in sphere
  The sphere is an inscribed cube with an edge of 8 cm. Find the sphere's radius.
• Spherical segment
  The spherical segment with height h=1 has a volume V=223. Calculate the radius of the sphere of which is cut this segment.