Q077 - Physics For Engineers And Scientists - Solutions

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Question 77 - Review - Chapter 1

Problem:

For many years there was a speed limit in the United States on the federal highways of 55 mi / h

Question:

a) How much is this in km / h?
b) How much is this in feet per second?
c) How much is this in m / s?

Solution:

One mile = 1.609 km

In [1]:
# Berekeningen
mile_km = 1.60934
speed_mi_h = 55
speed_km_h = speed_mi_h * mile_km
print(f'The speed in km/h = {speed_km_h:5.3} km/h')
The speed in km/h =  88.5 km/h

One feet = 0.3048 m = 3.048e-4 km

One hour = 3600 seconds

In [2]:
feet_km = 3.048e-4
hour_sec = 3600
speed_feet_h = speed_km_h / (hour_sec * feet_km)
print(f'The speed in Feet per second = {speed_feet_h:.2g} ft/s')
The speed in Feet per second = 81 ft/s
In [3]:
km_m = 1e-3
speed_m_s = speed_km_h / (hour_sec * km_m)
print(f'The speed in meter per second = {speed_m_s:.2g} m/s')
The speed in meter per second = 25 m/s

Alternative solution:

Alternatively we can make python do the conversion fully automatic by using Library Pint

The correct calculation and conversion is done entirely with the built-in logic.

In [4]:
# Same using Pint unit conversion lybrary
from pint import UnitRegistry
ureg = UnitRegistry()
speed_mi_h = 55 * ureg.mi / ureg.hour
speed_km_h = speed_mi_h.to(ureg.km / ureg.hour)
speed_ft_s = speed_mi_h.to(ureg.feet / ureg.sec)
speed_m_s = speed_mi_h.to(ureg.m / ureg.sec)
print(f'The speed in mi/h = {speed_mi_h:5.3}')
print(f'The speed in km/h = {speed_km_h:5.3}')
print(f'The speed in ft/s = {speed_ft_s:5.3}')
print(f'The speed in m/s = {speed_m_s:5.3}')
The speed in mi/h = 55.0 mile / hour
The speed in km/h = 88.5 kilometer / hour
The speed in ft/s = 80.7 foot / second
The speed in m/s = 24.6 meter / second

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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