101 Range Versus Height We say that an object undergoes free fall when the acceleration is only due to gravity. An object that is in free fall experiences a constant gravitational acceleration 푔 that points towards the ground. The object may travel along a complicated two-dimensional path but its motion can be decomposed into two independent one-dimensional motions. Gravity acts only in the vertical (y) direction and therefore there is no acceleration in the horizontal (x) direction. Using this information, we can write expressions for the position and velocity of the object as a function of t

vₓ = v₀ₓ ,                 x = x₀ + v₀ₓ t

= v_{y} - g t,     y = y₀ + v_{oy}  t - ½ g t²

Explanation:

The kinematic equations in one dimension are

            v = v₀ + a t

            x = x₀ + v₀ t + ½ a t²

In the case of two dimensions we can separate the movement into two independent components,

X axis

In this axis there is no acceleration (a= 0), therefore the equations remain

             vₓ = v₀ₓ

             x = x₀ + v₀ₓ t

The subscript x is entered to indicate the direction of movement

Y Axis

In this case there is an acceleration that points down

            a = - g

The equations remain

            = The kinematic equations in one dimension are

            .v = vo + a t

            .x = xo + vo t + ½ to t2

In the case of two dimensions we can separate the movement into two independent components,

X axis

In this axis there is no acceleration, therefore the equations remain

             .vx = vox

               .x = xo + vox t

The subscript x is entered to indicate the direction of movement

Axis and In this case there is an acceleration that points down

            .a = - g

The equations remain

            = v_{y} - g t

           y = y₀ + v_{oy}  t - ½ g t²

The subscript and indicates the direction of movement

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