Question

One cubic centimeter of a typical cumulus cloud contains 430 water drops, which have a typical radius of 10 μm. (a) How many cubic meters of water are in a cylindrical cumulus cloud of height 3.1 km and radius 1.1 km? (b) How many 1-liter pop bottles would that water fill? (c) Water has a density of 1000 kg/m³. How much mass does the water in the cloud have?

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 = 5.0t^0.8 - 2.6t + 20, 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 = 2.4 s and (d) t = 4.8 s?

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 , with t ≥ 0, m in grams, t in seconds, and A, B, and C positive constants. In terms of A, B, C and t, (a) find a formula for the rate of mass change as a function of t. (b) At what time is the water mass greatest, and (c) what is that greatest mass?

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 766 miles (in the United States), how many gallons of fuel does (a) the mistaken tourist believe she needs and (b) the car actually require?

One molecule of water (H₂O) contains two atoms of hydrogen and one atom of oxygen. A hydrogen atom has a mass of 1.0 u and an atom of oxygen has a mass of 16 u, approximately. (a) What is the mass of one molecule of water? (b) How many molecules of water are in the world's oceans, which have an estimated total mass of 1.4 × 10²¹ kg?

An astronomical unit (AU) is the average distance between the Earth and the Sun, approximately 1.50 × 10⁸ km. The speed of light is about 3.00 × 10⁸ m/s. Express the speed of light in astronomical units per minute.

An astronomical unit (AU) is equal to the average distance from Earth to the Sun, about 92.9 × 10⁶ mi. A parsec (pc) is the distance at which a length of 1 AU would subtend an angle of exactly 1 second of arc (the figure). A light-year (ly) is the distance that light, traveling through a vacuum with a speed of 186000 mi/s, would cover in 1.0 year. Express the Earth–Sun distance in (a) parsecs and (b) light-years.

Answer 1