Ella and April
Solution Set # 1
1. Meter—A meter is a unit of distance that is defined as the distance light
travels through a vacuum in 1/299,792,458 seconds.
a. Kilogram—A kilogram is a unit of mass that is defined by the
International Prototype Kilogram (IPK). The IPK is kept in the
International Bureau of Weights and Measures in Sèvres, France
and made from an alloy of 90% platinum and 10% iridium. It is the
only unit in the metric system that is still defined by a physical
object.
b. Second—A second is a unit of time that is defined by the natural
periodicity of the radiation of a cesium-133 atom. The Systeme
International d'Unites defines it like this because it allows time to
measured more accurately (on an atomic clock).
2. What Maxwell is saying is that if you have a length of one foot (1 ft), then
the area (when you extend a length by itself, creating a square) of that
length is 1 ft2—you have to square the unit as well as the numerical value
to make a square. If this were true, then a cube (or a length extended by
its self not only to create width, but to create depth) would have the
volume of 1 ft3, or one cubed foot.
a. The area of a square whose side is 6 inches is 36 inches2
b. The volume of a cube whose side is 6 inches is 216 inches3
3. 1 yard (3 feet; 36 inches) = 0.9144 meter & 100 centimeters = 1 meter
a. 4.2 yards = 3.84 meter
4.2 yard *
0.9144 𝑚𝑒𝑡𝑒𝑟
1 𝑦𝑎𝑟𝑑
= 3.84048 meter
b. 6 feet = 1.83 meter
(6 feet) 2 yards *
0.9144 𝑚𝑒𝑡𝑒𝑟
1 𝑦𝑎𝑟𝑑
= 1.8288 meter
c. 18.2 inches = 0.46228 meter
18.2 inches *
0.9144 𝑚𝑒𝑡𝑒𝑟
36 𝑖𝑛𝑐ℎ𝑒𝑠
= 0.46228 meter
d. 6.4 feet = 195.072 centimeters
6.4 feet *
0.9144 𝑚𝑒𝑡𝑒𝑟
3 𝑓𝑒𝑒𝑡
*
100 𝑐𝑒𝑛𝑡𝑖𝑚𝑒𝑡𝑒𝑟𝑠
1 𝑚𝑒𝑡𝑒𝑟
= 195.072 centimeters
4. 4. 1 mile = 1.6 kilometer = 1600 meters & 1 hour = 60 minutes = 3600
seconds
a. 60 miles/hour = 96 kilometers/hour
60 𝑚𝑖𝑙𝑒𝑠
1 ℎ𝑜𝑢𝑟
*
1.6 𝑘𝑖𝑙𝑜𝑚𝑒𝑡𝑒𝑟
1 𝑚𝑖𝑙𝑒
= 96 kilometers/hour
b. 3.2 meters/second = 7.2 miles/ hour
3.2 𝑚𝑒𝑡𝑒𝑟𝑠
1 𝑠𝑒𝑐𝑜𝑛𝑑
*
3600 𝑠𝑒𝑐𝑜𝑛𝑑𝑠
1 ℎ𝑜𝑢𝑟
1 𝑚𝑖𝑙𝑒
* 1600 𝑚𝑒𝑡𝑒𝑟𝑠 = 7.2 miles/hour
c. 0.5 mile/minute = 30 miles/hour
0.5 𝑚𝑖𝑙𝑒
1 𝑚𝑖𝑛𝑢𝑡𝑒
*
60 𝑚𝑖𝑛𝑢𝑡𝑒𝑠
1 ℎ𝑜𝑢𝑟
= 30 miles/hour
5.
a. Because the centimeter side of the ruler goes down to
millimeters, in comparison to the inch side of the ruler, it is much
more precise (because the graduations get smaller, you won’t
have to estimate as much as the inch side when measuring). A
possible reading would be 23.7 cm.
b. My lab partner would be wrong. The closest you can actually
measure on this ruler is one decimal place. However, it would
be considered valid if you estimated one more decimal place (if
necessary) and acknowledged it. In this case, my partner
estimates two decimal places, which is too hard to judge without
graduations, and the chances of him being right are highly
unlikely.
c. The inch scale of the ruler is not as precise as the centimeter
because it goes down to eighths. A possible reading would be
10 5/8 in.
d. 9 1/8 inches would be a valid answer. 9.125 is also a valid
answer because 9 1/8 is the same as 9.125 in fraction to
decimal form. Therefore, both of these answers are correct.