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Finally, solve for the magnitude and direction of the displacement and velocity using Recombine quantities in the horizontal and vertical directions to find the total displacement and velocity.The problem-solving procedures here are the same as those for one-dimensional kinematics. Note that the only common variable between the motions is time, t. Solve for the unknowns in the two separate motions.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.
![projectile motion equation projectile motion equation](https://blogmedia.testbook.com/blog/wp-content/uploads/2019/11/projectile-motion-formula-testbook-388cfdcc.png)
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.
![projectile motion equation projectile motion equation](https://i.ytimg.com/vi/iWziOeVf4e4/maxresdefault.jpg)
The motion of a projectile along the horizontal and vertical directions can be analyzed independently by using the equations of motion.