Question

You wonder what altitude the plane reached when it was directly above the end of the runway and how far it travelled to get to that point.

You know the runway tarmac is 5500 metres long and approximate that when the plane left the ground, it took off at an angle of 40 degrees. The plane travelled along the runway for about 5000 metres.

What is the plane’s height vertically when it is directly above the end of the runway? How far did the plane travel to get to the point directly above the end of the runway?

Answer 1

you don't approximate, you estimate.

so, the plane was off the ground for the last 500 meters. At that point, it was at a height h, where

h/500 = tan40°

The plane's ascending distance d is

500/d = cos40°

Answer 2

When the plane is directly above the runway, it is at an altitude of 652.7m