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The solutions to assignment 3 of math 1030. It includes calculations for converting units of length and volume, as well as a problem involving the creation of a potion with given quantities of solid ingredients and cooking time. The document also includes conversion factors for various units.
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Name: Solutions
For the units below make a list of the fundamental units and a list of the derived units:
{ speed, acceleration, energy, length, time, volume }
Solution
Fundamental Units
length time
Derived Units speed acceleration energy volume
Convert the following:
(a) 1 kilometer into inches.
Solution The appropriate conversion factor here is:
2.54 cm = 1 in.
Using this we can compute the solution:
1 km
( (^1000) m
1 km
) ( (^100) cm
1 m
) ( (^1) in
) ≈ 39 , 370 in
(b) 10 gallons into liters.
Solution If we look up the conversion factor the appropriate one here is:
1 gallon = 3.785 liters
So, our calculation is:
10 gal
(
) = 37. 85 L
(c) 65 miles per hour into meters per second.
Solution The appropriate conversion factor here is:
1.609 km = 1 mile
And so our calculation is: ( 65 miles hour
) ( 1 hour 60 min
) ( 1 min 60 sec
) (^
) ( 1000 m 1 km
) ≈ 29. 05
m s
Amount of moondust required:
1 snarf ling
(
) ( 1 snarblat
. 7 L
) ( 3 goldblats snarblat
) ( 17 g goldblat
)
= 167. 57 g of moondust.
Amount of time required to cook:
1 snarf ling
(
) ( 1 snarblat
. 7 L
) ( 3 tocs snarblat
) ( 13 min tock
) ( 60 s min
)
≈ 7 , 688 seconds to cook.
An empty water tank is in the shape of a sphere with a radius of 24 meters. Water flows into the tank at a rate of 18 cubic yards per second. How many minutes will it take until the tank is full? 1 meter = 1.094 yards.
Solutions The total volume of the sphere is given by the formula for the volume of a sphere:
πr^3 =
π(24m)^3 = 57, 905. 8 m^3.
Our rate is in terms of cubic yards, so we have to convert our volume to cubic yards:
57 , 905. 8 m^3
(
) 3 = 75, 818. 3 yards^3
Now, to calculate the amount of time it requires, we just divide the total volume we need to fill by the rate:
t =
volume rate
75 , 818. 3 yards^3 18 yards^3 s
= 4, 212. 13 seconds ≈ 70 minutes.
