Question

One cubic centimeter of a typical cumulus cloud contains 430
water drops, which have a typical radius of 10 *μ*m.
**(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/m^{3}. 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* = 5.0*t*^{0.8} - 2.6*t* + 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 (H_{2}O) 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 × 10^{21}
kg?

An astronomical unit (AU) is the average distance between the
Earth and the Sun, approximately 1.50 × 10^{8} km. The
speed of light is about 3.00 × 10^{8} 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 × 10^{6} 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

One cubic centimeter of a typical cumulus cloud contains 370
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
2.9 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?

One cubic centimeter of a typical cumulus cloud contains 190
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
2.9 km and radius 1.0 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?

One cubic centimeter of a typical cumulus cloud contains 50 to
500 water drops, which have a typical radius of 10 μm. For that
range, give the lower value and the higher value, respectively, for
the following. (PLEASE write clearly)
(a) How many cubic meters of water are in a cylindrical cumulus
cloud of height 2.5 km and radius 1.5 km?
______ to ________m^3
(b) How many 1-liter pop bottles would that water
fill?
______ to ________ bottles
(c) Water...

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