Answer to Question #4489 in Differential Equations for zirhyl

Question

Can anyone help me with this question? I've been trying to find ways to solve it but I have not found the correct way on how to. I hope you can help me with this question.

"Two points are moving horizontally in space at different heights above the earth. Show that the angle of elevation of the line joining them is greater when the distance between them is least."

Answer 1

Let's make some conclusions. First of all, the distance between two points, with different heights, is least when one of them is right under another. So If this condition occurs, the line, which join these two points, will make right angle with the surface. This is the greatest possible angle - 90º.