Interpreting Velocity Vectors in Projectile Motion?

📌 CONCEPT: In projectile motion, the velocity vector of a particle can be represented as a sum of its horizontal and vertical components, each with a magnitude and direction, which together determine the trajectory of the particle.

📐 RULE / FORMULA: The horizontal component of the velocity vector remains constant, while the vertical component is affected by the acceleration due to gravity, and can be represented as v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is time.

💡 WORKED EXAMPLE: A particle is projected with an initial velocity of 25 m/s at an angle of 60° to the horizontal. 2 seconds after projection, the horizontal component of its velocity remains 25 m/s, while the vertical component is affected by the acceleration due to gravity, and can be calculated as v = 25 m/s - 9.8 m/s² × 2 s = -19.6 m/s.

⚠️ COMMON MISTAKE: Students often forget to account for the acceleration due to gravity when calculating the vertical component of the velocity vector, leading to an incorrect representation of the particle's trajectory.