A stone is thrown horizontally with velocity u m/s. How is its motion analyzed?

When a stone is thrown horizontally with velocity u m/s, its motion is analyzed as a case of projectile motion, where horizontal and vertical motions are considered separately.

Key Concept:

• The motion is divided into two independent components:
1. Horizontal motion
2. Vertical motion

Horizontal Motion:

• Initial velocity = u
• Acceleration = 0 (no force acting horizontally, neglecting air resistance)
• Equation:
  x = ut

Vertical Motion:

• Initial velocity = 0 (since it is thrown horizontally)
• Acceleration = g (due to gravity, downward)
• Equation:
  y = (1/2)gt²

Resultant Path:

• The combination of horizontal and vertical motion produces a parabolic path.

Time of Flight:

• Depends only on the height (h) from which the stone is thrown:
  t = √(2h/g)

Range (Horizontal Distance):

• Range = u × t

Conclusion:
The motion of a horizontally thrown stone is analyzed using projectile motion principles, treating horizontal and vertical components independently, resulting in a parabolic trajectory.