The velocity and acceleration of a projectile at different points in its trajectory can be determined by analyzing the motion in both the horizontal and vertical directions.
Horizontal Motion:
- The velocity of a projectile remains constant throughout its horizontal motion.
- The horizontal velocity (Vx) remains unchanged since there is no horizontal acceleration (assuming no air resistance or other external forces).
- The horizontal velocity is given by Vx = V * cos(θ), where V is the initial velocity magnitude and θ is the launch angle.
Vertical Motion:
- The vertical velocity (Vy) changes due to the acceleration due to gravity.
- The acceleration due to gravity (g) is constant and acts downward with a magnitude of approximately 9.8 m/s^2.
- The vertical velocity changes at a constant rate due to the acceleration due to gravity, resulting in a parabolic trajectory.
- The initial vertical velocity (Vy0) is given by Vy0 = V * sin(θ), where V is the initial velocity magnitude and θ is the launch angle.
- The vertical velocity at any time (t) during the projectile's flight can be calculated using Vy = Vy0 - g * t.
- The vertical acceleration remains constant and is equal to -g.
It's important to note that the horizontal and vertical motions of a projectile are independent of each other. The horizontal velocity remains constant, while the vertical velocity changes due to the acceleration of gravity.