Q081 - Physics For Engineers And Scientists - Solutions

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Amateur Radio and Astronomy website. JO10UX

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.

Can the plane land?

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*} $

In [1]:
# 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 !


سُوۡرَةُ حٰمٓ السجدة / فُصّلَت
ثُمَّ اسْتَوَىٰ إِلَى السَّمَاءِ وَهِيَ دُخَانٌ فَقَالَ لَهَا وَلِلْأَرْضِ ائْتِيَا طَوْعًا أَوْ كَرْهًا قَالَتَا أَتَيْنَا طَائِعِينَ ﴿١١
فَقَضَاهُنَّ سَبْعَ سَمَاوَاتٍ فِي يَوْمَيْنِ وَأَوْحَىٰ فِي كُلِّ سَمَاءٍ أَمْرَهَا ۚ وَزَيَّنَّا السَّمَاءَ الدُّنْيَا بِمَصَابِيحَ وَحِفْظًا ۚ ذَٰلِكَ تَقْدِيرُ الْعَزِيزِ الْعَلِيمِ ﴿١٢


Surah Fussilat: Thereafter turned He to the heaven and it was as smoke, and said Unto it and Unto the earth: come ye twain, willingly or loth. They said: we come willingly. (11) Then He decreed them as seven heavens in two days, and revealed Unto each heaven the command thereof; and We bedecked the nether heaven with lamps and placed therein a guard. That is the ordinance of the Mighty, the Knower. (12)

De hemelen en aarde (waren) een samenhangende massa. Wij hebben ze toen van elkaar gescheiden… Wij hebben de hemel tot een beschermend dak gemaakt … en de dag en de nacht, de zon en de maan geschapen. (Koran 41 11:12)


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