Use the kinematic equations for horizontal and vertical motion presented earlier.

Treat the motion as two independent one-dimensional motions: one horizontal and one vertical.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. The magnitudes of the components of displacement along these axes are x and y. Initially, resolve the motion into horizontal and vertical components along the x- and y-axes.For example, a basketball thrown by a player, an arrow shot from a bow, and kids jumping into the pool, all undergo projectile motion.Īny projectile motion problem can be solved by using the following strategy: Projectile motion is commonly observed in our day-to-day life. Rearranging the terms in x-component equation and substituting it in the equation of y-position, we get the final trajectory equation. Its equation can be obtained by using the position equations. The trajectory describes the projectile's path in a 2-dimensional space. By substituting the total time in the displacement equation in the x-direction, the equation for the maximum range of the projectile is obtained. The total duration of the flight is twice the time of half-flight.

The zenith height of the projectile can be obtained by substituting the expression for the half-flight time in the displacement equation for y-direction.

By substituting v y in the velocity equation for y-direction, time for half-flight is obtained. The initial velocity components obtained by using trigonometric relations further simplify the motion equations.Īt the zenith, v y is zero. Putting a y as minus g and a x as zero for a projectile, the equations simplify. The motion of a projectile along the horizontal and vertical directions can be analyzed independently by using the equations of motion.

Projectile motion formula