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Puzzle challenge - distance to horizon

Image Analyst on 23 Mar 2024

Latest activity Reply by Image Analyst on 17 May 2024

In one line of MATLAB code, compute how far you can see at the seashore. In otherwords, how far away is the horizon from your eyes? You can assume you know your height and the diameter or radius of the earth.

8 (last 30 days)

8 Comments

BigZ on 15 May 2024

This is ai answer:

radius = 6371; % radius of the Earth in kilometers

height = 1.7; % height of the observer in meters

distance = sqrt(2 * radius * height + height^2);

distance = distance / 1000; % convert distance to kilometers

disp(['The distance to the horizon is approximately ', num2str(distance), ' kilometers.']);

%The distance to the horizon is approximately 0.14719 kilometers.

Image Analyst on 15 May 2024 (Edited on 15 May 2024)

Looks like no one else is going to post a response. This is the answer I got. Approximately 3 miles or 4.8 km.

D = 12742000; % Earth's diameter in meters.
R = D / 2; % Earth's radius in meters.
h = 1.8; % Your height in meters
% (R+h)^2 = d^2 + R^2
% d^2 = (R+h)^2 - R^2
distanceInMeters = sqrt((R+h)^2 - R^2)
dInMiles = distanceInMeters / 1609.34

distanceInMeters =

4789.1

dInMiles =

2.9758

Plug the numbers in directly to get the whole answer in one line of code.

1 Reply

goc3 on 15 May 2024

Using the constants provided in your answer, as well as the simplification mentioned by Christian, I wrote the following single-line anonymous function:

distance_in_miles = @(h) sqrt(h.*(h+12742000))./1609.34;

Since element-wise operators are used, it can take vector input and yield vector output, like the following:

height_in_meters = [0.3, 1.0, 1.8, 10, 30];
distance_in_miles(height_in_meters) = 
    1.2149    2.2180    2.9758    7.0141   12.1488

So, an infant sitting on the beach would be able to see more than a mile, a 1m-tall child over two miles, and an adult about three miles. On the other hand, looking out from a hotel room, perhaps on the third floor, would yield a view of about seven miles while a room on a much higher floor, perhaps the ninth, might result in a view of about 12 miles.