Explain the path of projectile motion along with force vectors and also labels

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Projectile motion is the motion of an object launched into the air under the influence of gravity. When we throw a ball or fire a cannonball, it follows a curved path called a trajectory. This path is parabolic in shape when we ignore air resistance. The projectile starts with an initial velocity vector and is constantly acted upon by the force of gravity pointing downward. After the projectile is launched, the only significant force acting on it is gravity. This gravitational force has a constant magnitude of mg, where m is the mass and g is the acceleration due to gravity. Notice that at every point along the trajectory, the force vector points straight downward with the same magnitude. This constant downward force creates a constant downward acceleration, which is why the projectile follows a parabolic path. The velocity vectors show the instantaneous direction and speed of the projectile at each point. Notice that these vectors are always tangent to the trajectory. The horizontal component of velocity remains constant throughout the flight because there are no horizontal forces acting on the projectile. However, the vertical component changes continuously due to the downward gravitational acceleration. At the peak of the trajectory, the vertical velocity becomes zero, while the horizontal velocity remains unchanged. Now let's watch the projectile in motion. As the projectile moves along its parabolic path, notice how the velocity vector continuously changes direction while the force vector remains constant, always pointing downward. The velocity vector starts with both horizontal and vertical components, becomes purely horizontal at the peak, and then gains a downward vertical component as the projectile descends. Throughout this entire motion, gravity provides the only force acting on the projectile. To summarize projectile motion: The trajectory is always parabolic when air resistance is ignored. Only gravity acts on the projectile after launch, providing a constant downward force. The velocity vector changes continuously in direction, with the horizontal component remaining constant while the vertical component changes due to gravitational acceleration. At launch, velocity has both components. At the peak, only horizontal velocity remains. At landing, the projectile has regained vertical velocity in the downward direction. This fundamental understanding applies to all projectile motion scenarios.