miscalculation.
Second, make a rough estimate. At what sorts of distances might a satellite orbit? We can
eliminate A immediately: that answer has our satellite orbiting at 4 cm from the center of the
Earth! That leaves us with a choice between B and C. Those aren’t bad odds for guessing.
Slightly Underhanded Way #2: Work with the Letters
This is a method for those of you who like manipulating equations. From looking at the answer
choices, you know the answer will be in meters. You’ve been given three quantities, one expressed
in m/s, one expressed in kg, and one expressed in N·m^2 /kg^2. These are the only three quantities
you’ll be asked to draw upon in order to get your answer. Because F = ma, you know you can
substitute kg·m/s^2 for N. So a quantity expressed in N·m^2 /kg^2 can equally be expressed in m^3 /kg·s^2.
The trick, then, is to combine a quantity expressed in these terms with a quantity expressed in
meters per second and a quantity expressed in kilograms, and wind up with a quantity expressed
solely in meters. To do that, you need to get rid of the “kg” and the “s” by canceling them out.
Start by canceling out the “kg”:
Now you need to cancel out the “s^2 ” in the denominator. Let’s divide by the square of our “m/s”
quantity:
There you have it. You didn’t need to use a single formula to get the answer. You just had to be
aware of the terms in which your answer needed to be expressed, and manipulate the quantities
you were given in the question.
Word to the wise: don’t use this method unless you’re absolutely stumped. It can backfire, and is
of course no substitute for careful reasoning.
Vectors
VECTORS ARE USUALLY THE FIRST THING you learn in a physics class, and they’re the first
thing you’ll learn here. Vectors are one of the fundamental mathematical tools the physicist uses,
and one that is frequently misunderstood or misapplied by students. Generally, there aren’t more
than one or two questions on SAT II Physics that test your knowledge of vectors directly, but there
are a host of problems—particularly in mechanics—where arriving at the right solution demands a
solid grasp of how to apply and manipulate vectors. Even if you feel confident with vectors, we
urge you to review this chapter and be absolutely sure you won’t get tripped up on what would
otherwise be some easy questions.
What’s a Vector?
A vector is a mathematical object possessing, and fully described by, a magnitude and a
direction. It’s possible to talk about vectors simply in terms of numbers, but it’s often a lot easier
to represent them graphically as arrows. The vector’s magnitude is equal to the length of the
arrow, and its direction corresponds to where the arrow is pointing. Physicists commonly refer to
the point of a vector as its tip and the base as its tail.