The distance l from a point at a height h above the Earth's surface to the horizon can be approximated using Pythagoras' theorem by the expression: (Please see the attachment below)
(a) Find an expression which serves as a linear approximation for l at h=1000 m.
(b) Give two assumptions you think have been made in deriving the expression above.© BrainMass Inc. brainmass.com March 4, 2021, 5:36 pm ad1c9bdddf
Please see the attachment below for the complete solution.
The above equation can be written in a more useful form as:
l = (h^2+2rh)^1/2
Taking the derivative of l with respect to h gives:
dl/dh = ...
This shows how to perform linearization of a function related to the Pythagorean theorem. Two assumptions for deriving the expressions are provided.