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Two-dimensional motion
Beginner
Independent horizontal and vertical motion combined.
In 2-D, horizontal and vertical motions are independent: apply the equations separately to each axis, linked only by time. Perpendicular components do not influence each other.
A ball rolling off a table keeps its horizontal speed while falling.
Don't mix x and y quantities in one equation.
In more detail
Two-dimensional motion is described using components along two perpendicular axes. Each component can be treated separately when acceleration is along one axis only.
Real-world uses
- Robot arms plan motion in the plane using separate x and y components.
- Aircraft navigation uses horizontal and vertical components of velocity.
- A basketball shot is a two-dimensional motion, with steady horizontal speed and a changing vertical speed under gravity.
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Frequently asked questions
Can I treat x and y separately?
Yes, when forces or accelerations act along each axis separately, which is true in projectile motion.
How do I find the speed in 2D?
Use the magnitude of the velocity vector, the square root of the sum of the squares of its components.
Are horizontal and vertical motions independent?
Yes, in the absence of air resistance. Gravity acts only vertically, so the horizontal velocity stays constant.
Related topics in Kinematics
Non-uniform acceleration · Motion graphs from calculus · Terminal velocity · Projectile motion · Time of flight · Maximum height