# Chapter 1 - Worked Solutions

### to selected Complex Reasoning questions from the OUP text *Senior Physics - Knowledge, Processes and Reasoning* by Walding, Rapkins and Rossiter

**Question 36**

3 x 10^{8} m ¸ 0.305 = 9.84 x 10^{8} feet

9.84 x 10^{8} feet ¸ 5280 = 186 289.12 miles

186 289.12 miles x 8 = 1 490 313 furlongs

1 fortnight = 14 days

14 days = 14 x 24 x 60 x 60 seconds = 1 209 600 s

In 1 fortnight light travels 1 490 313 x 1 209 600 furlongs = 1.8 x 10^{12} furlongs/fortnight.

**Question 37**

length = 756.5 ± 0.5 mm = 756.5 ± 0.07%

mass = 8.5 ± 0.5 g = 8.5 ± 6%

mass/mm = 8.5/756.5 = 1.1236 x 10^{-12} ± (6 + 0.07)%

= 1.1236 x 10^{-12} ± 6.8 x 10^{-4}

= 1.1 x 10^{-12} (2SF) ± 7 x 10^{-4} (1SF) g/mm

**Question 38**

time = distance ¸ speed = 10^{-15} ¸ 3 x10^{8} = 3 x 10^{-24} s

In 1 second there are 1 ¸ (3 x 10^{-24}) fermis = 3 x 10^{23} fermis in 1 second.

**Question 39**

$36 000 per year = $690 per week (2SF)

**Question 40**

Total number of bytes = 200 x 2^{20} = 200 x 1048576 = 2097152 or 2.097152 x 10^{8
}Number of 8 byte words = 2.097152 x 10^{8} / 8 = 2.6214400 x 10^{7} words.

This is written as 3 x 10^{7} to one significant figure.

NOTE: There is an error in the question. A 'word' is actually __two__ bytes not eight. There are 8 bits to a byte.

Question 41

The metre was defined as a particular length in 1983 and the speed of light measured in reference to this. The speed of light is a measured quantity, not a defined one like the metre or the second.

**Question 42
**
- Christians want to commemorate Easter on the correct day (actually - the first Sunday after the first full moon after the vernal equinox). This Sunday has to be correct.
- 10 days adrift so March 1 in Moscow would be March 11 in London;
- After 407 years there is a drift of 169 minutes so after 423 years the drift would be 169 x 423/407 = 176 minutes (2 h 56 m).

Question 43

Volume of 1 drop = 1/20 mL = 0.05 cm^{2}

Area of drop = pr^{2 }
= 3.14 x 7^{2} = 153.9 cm^{2
}Volume = A x ht; ht = V/A = 0.05/153.9 = 3.25 x 10^{-4} cm =
3.25 x 10^{-6} m (= 3.25 mm).

Question 44

No. molecules in glass = 250mL/18 x 6
x 10^{23} = 8.33 x 10^{24}.

No. glasses in oxcean = (1.3 x 10^{18} x 1000)/0.250L = 5.2 x 10^{21
}Answer: true - more in glass.

Question 45

Volume = 4/3 pr^{3}
= 4/3 p (20 x 10^{3} x 10^{2})^{3}
= 3.35 x 10^{19} cm^{3}.

D = m/V = (2 x 10^{30 })/(3.35 x 10^{19} )= 5.97 x 10^{10}
kg/cm^{3}.

*Return to Physics Text Home Page*