Projectile Motion: Equations

Projectile motion is commonly observed in our day-to-day life. For example, a basketball thrown by a player, an arrow shot from a bow, and kids jumping into the pool, all undergo projectile motion.

Any projectile motion problem can be solved by using the following strategy:

1. Initially, resolve the motion into horizontal and vertical components along the x- and y-axes. The magnitudes of the components of displacement along these axes are x and y. The magnitudes of the vertical and horizontal components of velocity are given by v⋅sin(θ) and v⋅cos(θ), respectively, where v is the magnitude of the velocity and θ is its direction relative to the horizontal.
2. Treat the motion as two independent one-dimensional motions: one horizontal and one vertical. Use the kinematic equations for horizontal and vertical motion presented earlier.
3. Solve for the unknowns in the two separate motions. Note that the only common variable between the motions is time, t. The problem-solving procedures here are the same as those for one-dimensional kinematics.
4. Recombine quantities in the horizontal and vertical directions to find the total displacement and velocity. Finally, solve for the magnitude and direction of the displacement and velocity using

where θ is the direction of the displacement.

This text is adapted from Openstax, University Physics Volume 1, Section 4.3: Projectile Motion.