1-Hydraulic engineers in the United States often use, as a units of volume of water, the acre-foot, defined as the volume of water that will cover 1 acre (where 1 acre = 43560 ft2) of land to a depth of 1 ft. A severe thunderstorm dumped 2.1 in. of rain in 30 min on a town of area 39 km2. What volume of water, in acre-feet, fell on the town?
2-Because Earth’s rotation is gradually slowing, the length of each day increases: The day at the end of 1.0 century is 1.0 ms longer than the day at the start of the century. In 29 centuries, what is the total of the daily increases in time (that is, the sum of the gain on the first day, the gain on the second day, etc.)?
3-Grains of fine California beach sand are approximately spheres with an average radius of 50 μm and are made of silicon dioxide, which has a density of 2.4 × 103 kg/m3. What mass of sand grains would have a total surface area (the total area of all the individual spheres) equal to the surface area of a cube 1.0 m on an edge?
4-During heavy rain, a section of a mountainside measuring 4.8 km horizontally (perpendicular to the slope), 0.42 km up along the slope, and 0.58 m deep slips into a valley in a mud slide. Assume that the mud ends up uniformly distributed over a surface area of the valley measuring 1.1 km x 1.1 km and that the mass of a cubic meter of mud is 1900 kg. What is the mass of the mud sitting above a 4.8 m2 area of the valley floor?
5-Water is poured into a container that has a leak. The mass m of the water is given as a function of time t by m = 5.3t0.8 – 2.6t + 19, with t ≥ 0, m in grams, and t in seconds. (a) At what time is the water mass greatest, and (b) what is that greatest mass? What is the rate of mass change at(c) t = 1.9 s and (d) t = 5.0 s?
6-A vertical container with base area of length L and width W is being filled with identical pieces of candy, each with a volume of v and a mass m. Assume that the volume of the empty spaces between the candies is negligible. If the height of the candies in the container increases at a certain rate per unit time dH/dt, at what rate per unit time does the mass of the candies in the container increase?
dM/dt =
7-A tourist purchases a car in England and ships it home to the United States. The car sticker advertised that the car’s fuel consumption was at the rate of 40 miles per gallon on the open road. The tourist does not realize that the U.K. gallon differs from the U.S. gallon:
1 U.K. gallon = 4.545 963 1 liters
1 U.S. gallon = 3.785 306 0 liters
For a trip of 765 miles (in the United States), how many gallons of fuel does (a) the mistaken tourist believe she needs and (b) the car actually require?
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