Chapter-2 Q029 - Physics For Engineers And Scientists - Solutions

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Amateur Radio and Astronomy website. JO10UX

Question 29 - Problems - Chapter 2

Problem:

A messenger carries a package twelve city blocks north in 14 min 5 s.

There, she receives a second package, which she brings six blocks south in 6 min 28 s.

Finally, she gets a third package, which she brings 3 blocks north in 3 min 40 s.

The city block spacing is 81 m. what is her average speed?What is her average velocity?

Question:

a) What is her average speed?

b) What is her average velocity?

Solution:

$\bigtriangleup t_1 = 14m 5s$

$\bigtriangleup t_2= 6m 28s$

$\bigtriangleup t_3= 3m 40s$

One Block = 81m

$\bigtriangleup s_1 = 12x81m=972m$

$\bigtriangleup s_2 = -6x81m=-486m$

$\bigtriangleup s_2 = 3x81m=243m$


The total displacement $\bigtriangleup s = \bigtriangleup s_1 + \bigtriangleup s_4 + \bigtriangleup s_5$

The average velocity:

$$ \overline v=\frac{\bigtriangleup s}{\bigtriangleup t} $$

Total distance $s = \Big|{{\bigtriangleup s_1}}\Big| + \Big|{\bigtriangleup s_2}\Big| + \Big|{\bigtriangleup s_3}\Big|$

The average speed is

$$ v = \frac{s}{t} $$

The problem is almost the same as problem Q028, so we can reuse the same program by just changing the values of the parameters.

In [1]:
import numpy as np
t1 = 14*60 + 5
t2 = 6*60 + 28
t3 = 3*60 + 40
d_s1 = 972
d_s2 = -486
d_s3 = 243
v_s = (np.abs(d_s1) + np.abs(d_s2) + np.abs(d_s3)) / (t1 + t2 + t3)
v_v = (d_s1 + d_s2 + d_s3) / (t1 + t2 + t3)
print(f'The average speed is: {v_s:.2f} m/s')
print(f'The average velocity is: {v_v:.2f} m/s')
The average speed is: 1.17 m/s
The average velocity is: 0.50 m/s

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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