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**preview**has**blurred**sections. Sign up to view the full version! View Full DocumentHow Many Drops in All the Oceans?
Part A
How many drops of water are in all the oceans on earth? Assume that
contains 25
drops of water. Remember that this is an order-of-magnitude problem, so you should expect
that you will only find rough estimates for the numbers you require.
Hint A.1 Mean depth of the oceans
The mean (average) depth of the oceans is about
.
Hint A.2 Radius of the earth
The radius of the earth is about
.
Hint A.3 Percent of the earth covered by ocean
About 70% of the earth is covered by oceans.
Hint A.4 Surface area of a sphere
The surface area
of a sphere with radius
is given by the formula
.
Express your answer to one significant figure.
ANSWER:
4.0×10
25
Correct
drops
Although order-of-magnitude calculations may seem silly at times, they are a major tool
used by physicists. Any time that you are solving a problem in physics, it is helpful to have
an estimate in your head of the order of magnitude that you expect from the answer. For
instance, if you were trying to find the average speed of a car over a long trip and got an
answer of 1000 miles per hour, you would immediately know that you had done something
wrong, because your answer has the wrong order of magnitude.
Order-of-magnitude problems are sometimes called Fermi problems, after the physicist
Enrico Fermi who was reportedly a master of such approximate calculations. When the first
atomic bomb was tested, Fermi was able to get a rough estimate of the power that the bomb
released by throwing some torn bits of paper into the air as the pressure wave from the bomb
passed him and then performing a rough calculation.
Tracking a Plane
A radar station, located at the origin of
xz
plane, as shown in the figure

station from the east. At first observation (point A), the position of the airplane relative to the
origin is
. The position vector
has a magnitude of 360
and is located at exactly 40
above the horizon. The airplane is tracked for another 123
in the vertical east-
west plane for 5.0 , until it has passed directly over the station and reached point B. The
position of point B relative to the origin is
(the magnitude of
is 880
). The contact
points are shown in the diagram, where the
x
axis represents the ground and the positive
z
direction is upward.
Part A
Define the displacement of the airplane while the radar was tracking it:
.
What are the components of
?
Hint A.1 How to approach the problem
Keep in mind that
.According to the rules of vector addition and
subtraction, the
x
component of
is
.
Hint A.2
Finding the components of
What are the components of
in the
and
directions?
Express your answer in meters as an ordered pair, separating the
x
and
z
values with
commas, to three significant figures.
ANSWER:

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