2D and 3D Motion

The position vector is expressed through its Cartesian coordinates.

The vector displacement is the difference between the final and initial positions.

Ratio of the vector displacement to the elapsed time interval.

Derivative of the position vector with respect to time.

Derivative of the velocity vector with respect to time.

Horizontal and vertical components of a projectile's initial velocity.

Horizontal position of a projectile with zero horizontal acceleration.

• without air resistance; $a_x=0$.

Vertical position of a projectile with constant gravitational acceleration.

Vertical component of a projectile's velocity as a function of time.

The horizontal component of a projectile's velocity remains constant.

• without air resistance.

Time elapsed until the projectile's vertical velocity vanishes.

• $v_y=0$ at the peak.

additional height with respect to the launch point.

Flight time of a projectile that returns to the same launch height.

• arrival point at the same height as the launch point.

Horizontal range of a projectile that starts and lands at the same height.

• same initial and final height, horizontal surface, and negligible air resistance.

Relative velocity is obtained by composing velocities with respect to intermediate frames.