Question 81 - Review - Chapter 1

Problem:

A small single-engine plane is flying at 5000m height and at an horisontal distance of 18 km from the airport of San-Francisco when the engine quits. The pilot knows that without engine he can glida at an downward angle of 15 degrees.

Question:

Can the pilot reach the airport?

Solution:

At a gliding scope of 15° (angle a) the maximal distance the plane kan reach is:

$ \begin{align*} & MaxDistance = \frac{\cos{a} * Height}{\sin{a}} \end{align*} $

# Calculations
import numpy as np
Height = 5000
a = 15
a_rad = (15/180) * np.pi
MaxDistance = (np.cos(a_rad) * Height)/np.sin(a_rad)
print(f'The Maximal Distance is {MaxDistance:.0f} m -or- {MaxDistance/1000:.1f} km')

The Maximal Distance is 18660 m -or- 18.7 km

So the pilot made it !