Understanding the Physics

* Horizontal motion: The stone's horizontal velocity remains constant throughout its flight because there's no horizontal force acting on it (ignoring air resistance).

* Vertical motion: The stone accelerates downwards due to gravity (g = 9.8 m/s²).

Calculations

1. Find the time of flight:

* We can use the vertical motion to determine the time it takes for the stone to fall 25.00 m.

* Use the equation: d = v₀t + (1/2)gt² (where d = distance, v₀ = initial vertical velocity = 0, g = acceleration due to gravity, and t = time)

* Rearranging for time: t = √(2d/g) = √(2 * 25.00 m / 9.8 m/s²) ≈ 2.26 s

2. Calculate the initial horizontal velocity:

* We know the horizontal distance traveled (40.00 m) and the time of flight (2.26 s).

* Use the equation: distance = velocity * time

* Rearranging for velocity: velocity = distance / time = 40.00 m / 2.26 s ≈ 17.70 m/s

Answer: The initial horizontal velocity of the stone was approximately 17.70 m/s.