Parabolic motion

The parabolic motion is the union of two simultaneous and independent straight motions, one uniform and one constantly accelerated.

Projectile motion with initial velocity and an angle θ In this case the projectile is constantly accelerated by the gravitational acceleration along the y axis, on the other axis the motion is uniform as there are no forces or accelerations.

斜方投射の運動.svg

INITIAL CONDITIONS:

SCOMPOSITION OF MOTION:

1. TAJECTORY

We obtain from [1] and we replace it in [2] to find :

2. RANGE

We impose in order to find the total horizontal displacement:

As
we find
which is the position of launch and
which is the range.

3. MAXIMUM HEIGHT

To find the maximum height we replace in the [2]:

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