Two-Dimensional Kinematics

Consider what happens when a ball rolls off the edge of a high table, as shown here. The ball follows a parabolic trajectory, which is indicative of the fact that the x and y motions are different. Ignoring air resistance, the horizontal motion is constant velocity while the vertical motion is constant acceleration.
The x and y components of velocity are shown as red and green arrows, respectively. The green arrow increases in length while the red arrow stays the same length as time goes on.
The kinematics equations for the two components are derived from the same three equations we used for uniformly accelerated motion in one-dimension. But only the x and y displacement equations are needed for the types of problems we will be doing.
The two displacement equations are linked by the variable t: time of flight. As long as we know vx and one of the displacements, we can solve for the other displacement by solving first for t.

Common pitfalls include: mixing up the x and y variables, solving for acceleration rather than taking the values as known (ax=0 and ay=+9.8 m/s2).

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