Math Is Fun Forum

tonyz1949

Member

Registered: 2007-08-04

Posts: 20

Physics math

1) An average family of four uses roughly 1200 liters (about 300 gallons) of water per day. (One liter = 1000 cm^3.) How much depth would a lake lose per year if it uniformly covered an area of 50 square kilometers and supplied a local town with a population of 40,000 people? Consider only population uses, and neglect evaporation and so on.

2) A heavy rainstorm dumps 1.0 cm of rain on a city 5 km wide and 8 km long in a 2-h period. How many metric tons (1 metric ton = 10^3 kg) of water fell on the city? [1 cm^3 of water has a mass of 1 gram = 10^-3 kg.] How many gallons of water was this?

3) Estimate how many days it would take to walk around the world, assuming 10 h walking per day at 4 km/h.

4) If you began walking along one of Earth’s lines of longitude and walked until you had changed latitude by 1 minute of arc (there are 60 minutes per degree), how far would you have walked (in miles)? This distance is called a “nautical mile.”

5) How big is a ton? That is, what is the volume of something that weighs a ton? To be specific, estimate the diameter of a 1-ton rock, but first make a wild guess: will it be 1 ft across, 3 ft, or the size of a car? [Hint: Rock has mass per volume about 3 times that of water, which is 1 kg per liter (10^3 cm^3) or 62 lb per cubic foot.]

6) Noah’s ark was ordered to be 300 cubits long, 50 cubits wide, and 30 cubits high. The cubit was a unit of measure equal to the length of a human forearm, elbow to the tip of the longest finger. Express the dimensions of Noah’s ark in meters, and estimate its volume (m^3).

7) One liter (1000 cm^3) of oil is spilled onto a smooth lake. If the oil spreads out uniformly until it makes an oil slick just one molecule thick, with adjacent molecules just touching, estimate the diameter of the oil slick. Assume the oil molecules have a diameter of 2x10^-10m.

8) Jean camps beside a wide river and wonders how wide it is. She spots a large rock on the bank directly across from her. She then walks upstream until she judges that the angle between her and the rock, which she can still see clearly, is now at angle of 30° downstream. Jean measures her stride to be about one yard long. The distance back to her camp is 120 strides. About how far across, both in yards and in meters, is the river?

9) A watch manufacturer claims that its watches gain or lose no more than 8 seconds in a year. How accurate is this watch, expressed as a percentage?

10)  The diameter of the Moon is 3480 km. What is the volume of the Moon? How many Moons would be needed to create a volume equal to that of Earth?

11) An angstrom is a unit of length, defined as 10^-10 m, which is on the order of the diameter of an atom.
(a)    How many nanometers are in 1.0 angstrom?
(b)    How many femtometers or fermis are in 1.0 angstrom?
(c)    How many angstrms are in 1.0 light year

12) How many angstroms are in 1.0 meter?

13) Determine the percent uncertainity in q, and in sin q, when
(a)    q = 15.0° +/- 0.5°

(b)    q = 75.0° +/- 0.5°

Thank you for helping. I figure this is a lot, but I appreciate your help.
This is a part of my Physics and I please need the answers.   
I know you will not let me down 

jon doe

Guest

Re: Physics math

A heavy rainstorm dumps 1.0 cm of rain on a city 5 km wide and 8 km long in a 2-h period. How many metric tons (1 metric ton = 10^3 kg) of water fell on the city?

5000 m * 8000 m * .01 m

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Physics math

On #7, the oil molecules could be in a rectangular array in X,Y,Z directions.
However, a tetrahedral compaction would be sqroot of 2 times more dense
according to my fun calculation that just brought me thru many memories
dating back to college, and the 3:1 ratio from
top-to-center-of-a-tetrahedron:center-to-base-of-tetrahedron ratio, and
also put the tetrahedron in a cube with the 4 vertexes of the tetrahedron
at 4 vertexes of the 8 of a cube.
The 2-D hexagonal arrangement in X-Y is easy, the parallelograms
are sqroot of 3 over 2 times more compact than a square grid.
The vertical component in the tetrahedron got fun to figure out.
My scribbles have:
(4/3)(√3/2)(1/√2) in it which reduces to √2/√3 for the vertical compaction.
But oil is not a crystal, but this is fun to think about...

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igloo myrtilles fourmis

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Physics math

On #4, the meridian that goes from antartica to northpole and back around to antartica
is around 40005 or 40008 km, which is 24859.8 miles or so.
For an estimate,  just divide this by 360 degrees and divide again by 60.
Should get 1.1509 miles.
However 60 times 1.1509 is the degree distance going north or south.
I found a chart that says it varies between
68.7 miles and 69.4 miles, but the chart had 90 and 0 backwards from
how I would have thought based on the values.
And wiki says a nautical mile is 1.1507794 miles, but stated in meters.

Last edited by John E. Franklin (2008-01-17 06:58:02)

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igloo myrtilles fourmis

phamthephong100

Member

Registered: 2007-10-13

Posts: 8

Re: Physics math

1) 0.0876m
2) 400000000 metric tons
    100000000 gallons
3) about 1001.875 days
others problems are so that even a primary student can solve all of them .you should solve them by youself
P/S my english is not very good