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?

1. A street light is supported by two wires and each makes a different angle from each other. The one on the left is 32 degrees and the one on the right is 43 degrees. Find the tension in each wire if the street light has a mass of 60.0 kg.
2. There are three masses m1 = 2.0 kg, m2 = 5.0 kg and m3 = 7.0 kg. The mass are all affixed to a massless rod of length 15cm. m1 and m3 are at the ends and m2 is 10 cm from left where m1 is. Calculate the center of mass of the system.
3. A pair of hedge trimmers are 45 cm long from the pivot to the end of the handles. If the person applies of a force of 15 N on each handle and the blades are 3.5 cm long, how much force is applied to the branch?
4. A 245 kg person lays on board that is supported only on the ends and that has a mass of 12.0 kg. If the person and the board are both 205 cm long and the person’s center of mass is 38 cm from the left side, what is the force on either side where the board is supported?
5. A large tank of water is full and has a depth of 10.0 m. What is the pressure at the bottom of the tank? What would the velocity of the water be if the tank was opened at the bottom?
6. A Two balloons of identical volume (radius 11.5 m) are filled with gas. The first with helium, the second with hydrogen (H2) gas. Each balloon and cage have a mass of 750 kg. What is the lift created by each one? Which one lifts better?
7. A irregular piece of metal has a dry mass of 5.7 kg. Once it is submerged it has an apparent mass of 2.4 kg. What is the density of the piece of metal?
8. If water leaves a tank of water at a velocity of 16.7 m/s, how tall is the tank?

A subway train starting from rest leaves a station with a constant acceleration. At the end of 7.55 s, it is moving at 17.818 m/s. What is the train’s displacement in the first 4.5753 s of motion? Answer in units of m
Exactly 2.7 after a projectile is fired into the air from the ground, it is observed to have a velocity = (8.2 + 4.7 ), where the axis is horizontal and the axis is positive upward What is the horizontal range of projectile.
the gravitational force between two objects that are 2.1×10^-1 m apart is 3.2×10^-6 N. if the mass of one object is 55 kg what is the mass of the other object?