Projectiles: Vertical Component

Introduction

• When analysing the motion of projectiles, it's essential to understand how the vertical component behaves.
• The vertical component of motion is characterised by a constant acceleration downwards due to gravity.

Vertical Acceleration

• In projectile motion, the vertical component experiences an acceleration directed downwards.
• On Earth, the acceleration due to gravity is approximately -9.8 m/s² (negative because it points downward).
• This acceleration affects the vertical velocity and position of the projectile.

Formula for Vertical Displacement

• The vertical displacement (d_vertical) of a projectile can be calculated using the formula:
• d_vertical = v_vertical_initial × t + 0.5 × a_vertical × t²
  • d_vertical: Vertical displacement
  • v_vertical_initial: Initial vertical velocity
  • t: Time of flight (total time the projectile is in the air)
  • a_vertical: Vertical acceleration due to gravity

Impact of Gravity on Vertical Motion

• Gravity's constant downward acceleration influences the vertical motion of a projectile.
• It causes the vertical velocity to decrease as the projectile rises and increases as it falls.
• At the highest point of the trajectory, the vertical velocity becomes zero momentarily.

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Projectiles: Vertical Component

Independence of Vertical and Horizontal Motion

• An essential concept in projectile motion is that the vertical and horizontal motions are independent of each other.
• While gravity affects vertical motion, it has no effect on the horizontal component of velocity.
• This means that the horizontal speed remains constant throughout the motion.

Applications

• Understanding the vertical component of motion is crucial in various real-world scenarios.
• It's essential for predicting the vertical displacement and time of flight of projectiles, such as objects launched into the air or fired at an angle.

Summary

• In projectile motion, the vertical component is characterised by a constant acceleration due to gravity, approximately -9.8 m/s² on Earth.
• This vertical acceleration affects the vertical velocity and displacement of the projectile.
• The vertical displacement can be calculated using the formula d_vertical = v_vertical_initial × t + 0.5 × g_vertical × t².
• The independence of vertical and horizontal motion means that gravity's influence on the vertical component does not affect the constant horizontal speed of the projectile.