Question

An person standing on a cliff 100 m above the ocean has a clear, unobstructed view of a small boat moving directly away from the point of observation. (a) How far away is the boat when it disappears over the horizon? (b) Explain how this phenomenon could be used to determine the radius of the Earth. A practice question...If someone can please explain this to me in some depth that would be great.

Answer 1

(a) we have relation As above formed triangle is Right angled triangle so

(R+x)²=R²+Y²  

here the radius of earth R=6.410⁶ m , height from where the object is seen x=100m (not considering the height of the person ), and the distnace where object is last visible .

(6.410⁶+100)²= (6.410⁶ )² + Y²

Y=3.610⁴ m ANS

(b) If we have knowledge of the the distace upto which the object is seen to the person then we can then using same equation

(R+x)²=R²+Y²

we can find the value of the radius of the earth .

(R+100)² =R²+(3.610⁴)²

200R+100² =(3.610⁴)²  

R=6.410⁶ m ANS