Q080 - Physics For Engineers And Scientists - Solutions

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Amateur Radio and Astronomy website. JO10UX

Question 80 - Review - Chapter 1

Problem:

A driveway up a hill has a slope of 1:9. We travel a horizontal distance of 300m

The slope on the hill

Question:

a) What is the ascend (in m)?
b) What is the corresponding distance measured along the way?

Solution:

If the slope is 1:9, the ascend is $\frac{1}{9}th$ of the horizontal distance.

For the distance along the way, we use Pythagoras:

$ \begin{align*} & way = \sqrt{distance^2 + ascend^2} \end{align*} $

In [1]:
# Calculations
import numpy as np
distance = 300
ascend = 1/9 * distance
print(f'The the ascend is {ascend:.0f} m')
way = np.sqrt(distance**2 + ascend**2)
print(f'The length of the way is {way:.0f} m')
The the ascend is 33 m
The length of the way is 302 m

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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