
TwoDimensional Motion with Uniform Acceleration
If you’ve got the hang of 1D motion, you should have
no trouble at all with 2D motion. The motion of any object moving
in two dimensions can be broken into x and ycomponents.
Then it’s just a matter of solving two separate 1D 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 ycomponents,
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/s^{2}. This is exactly the
kind of motion we examined in the previous section: if we ignore
the xcomponent, 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.
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 ycomponents 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 onedimensional
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 twodimensional motion is to remember that
you are not dealing with one complex equation of motion, but rather
with two simple equations.
