The resultant velocity of a projectile at any point in its trajectory can be determined by considering the horizontal and vertical components of its motion separately.
In the horizontal direction, a projectile's velocity remains constant throughout its entire flight. This is because there are no horizontal forces acting on the projectile (assuming negligible air resistance). Thus, the horizontal component of the resultant velocity remains unchanged.
In the vertical direction, the velocity of a projectile changes due to the influence of gravity. As the projectile moves upward, its vertical velocity decreases until it reaches its maximum height, where it momentarily becomes zero. On the way back down, the vertical velocity increases in the opposite direction until it reaches the same magnitude it had at the initial launch.
At any point during the projectile's flight, the resultant velocity is the vector sum of its horizontal and vertical velocities. This can be determined using vector addition. The magnitude of the resultant velocity is given by the Pythagorean theorem:
Resultant velocity = sqrt((horizontal velocity)^2 + (vertical velocity)^2)
The direction of the resultant velocity is determined by the angle between the horizontal direction and the resultant vector, which can be calculated using trigonometry.
To summarize, at any point in a projectile's trajectory, the resultant velocity is the vector sum of its horizontal and vertical velocities. The magnitude and direction of the resultant velocity can be determined using the appropriate equations and trigonometric calculations.