Math 1210-007
Planar Motion
Fall 2010
Planar Motion
Planar motion, or motion in two dimensions, can be analyzed in a very similar manner to the way
we analyzed one dimensional motion. Motion in the plane can be described independently in
terms of its vertical and horizontal components of motion. To give a general picture of how this
works let us introduce the following notation.
Horizontal Motion
Vertical Motion
= Horizontal Position
= Vertical Position
= Horizontal Velocity
= Vertical Velocity
= Horizontal Acceleration
= Vertical Acceleration
In the case when acceleration is constant in both directions, we can describe the position,
velocity, and acceleration more precisely.
The motion in the horizontal direction can be considered independently of the motion in the
vertical direction and vice versa. In most problems for this class, the acceleration in the vertical
direction will be the acceleration of gravity which is -32 ft./s2 (-9.8m/s2), and the acceleration in
the horizontal direction will be zero. The only situation in which this would be different is if
other forces were acting on the object, in which case you would use Newton's second law to
determine how these forces would cause the object to accelerate and in what direction. Then you
would use your knowledge of vectors to determine what its acceleration is for each component
(horizontal and vertical).
Once the acceleration of the object is understood in for both components, you then need to know
the initial velocity and position for each component. Often times a velocity will be expressed in
terms of a magnitude and direction (e.g. 100 m/s at a 45 angle). For those problems you would
use your knowledge of vectors to determine the horizontal and vertical components of initial
velocity.