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Two-Dimensional Motion with Uniform Acceleration
If you’ve got the hang of 1-D motion, you should have
no trouble at all with 2-D motion. The motion of any object moving
in two dimensions can be broken into x- and y-components.
Then it’s just a matter of solving two separate 1-D kinematic equations.
The most common problems of this kind on SAT II Physics
involve projectile motion: the motion of an object that is shot,
thrown, or in some other way launched into the air. Note that the
motion or trajectory of a projectile is a parabola.
If we break this motion into x- and y-components,
the motion becomes easy to understand. In the y direction,
the ball is thrown upward with an initial velocity of 
and
experiences a constant downward acceleration of g =
–9.8 m/s2. This is exactly the
kind of motion we examined in the previous section: if we ignore
the x-component, the motion of a projectile
is identical to the motion of an object thrown directly up in the
air.
and
experiences a constant downward acceleration of g =
–9.8 m/s2. This is exactly the
kind of motion we examined in the previous section: if we ignore
the x-component, the motion of a projectile
is identical to the motion of an object thrown directly up in the
air.In the x direction, the ball is thrown
forward with an initial velocity of 
and
there is no acceleration acting in the x direction
to change this velocity. We have a very simple situation where 
and 
is
constant.
and
there is no acceleration acting in the x direction
to change this velocity. We have a very simple situation where and is
constant.SAT II Physics will probably not expect you to do much
calculating in questions dealing with projectile motion. Most likely,
it will ask about the relative velocity of the projectile at different
points in its trajectory. We can calculate the x-
and y-components separately and then combine
them to find the velocity of the projectile at any given point:
Because 
is constant, the speed
will be greater or lesser depending on the magnitude of 
. To determine where the speed is least
or greatest, we follow the same method as we would with the one-dimensional
example we had in the previous section. That means that the speed
of the projectile in the figure above is at its greatest at position F,
and at its least at position C. We
also know that the speed is equal at position B and
position D, and at position A and
position E.
is constant, the speed
will be greater or lesser depending on the magnitude of . To determine where the speed is least
or greatest, we follow the same method as we would with the one-dimensional
example we had in the previous section. That means that the speed
of the projectile in the figure above is at its greatest at position F,
and at its least at position C. We
also know that the speed is equal at position B and
position D, and at position A and
position E.The key with two-dimensional motion is to remember that
you are not dealing with one complex equation of motion, but rather
with two simple equations.
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