1. Understand the Physics

* Projectile Motion: The rock is a projectile, meaning its motion is governed by gravity.

* Horizontal and Vertical Motion: We need to analyze the horizontal and vertical components of the motion separately.

* Constant Velocity: The horizontal velocity of the rock remains constant (ignoring air resistance).

* Acceleration due to Gravity: The vertical acceleration is due to gravity (g = 9.8 m/s²).

2. Calculate the Time of Flight

* Vertical Motion: We know the vertical distance (450 meters) and the acceleration due to gravity (9.8 m/s²). We can use the following kinematic equation to find the time it takes for the rock to hit the water:

* d = v₀t + (1/2)at² (where 'd' is distance, 'v₀' is initial vertical velocity, 't' is time, and 'a' is acceleration)

* Since the initial vertical velocity is zero (you kick the rock horizontally), the equation simplifies to:

* 450 m = (1/2)(9.8 m/s²)t²

* Solve for 't':

* t² = (450 m * 2) / 9.8 m/s²

* t ≈ 9.58 s

3. Calculate the Initial Horizontal Velocity

* Horizontal Motion: We know the horizontal distance (32 meters) and the time of flight (9.58 s). We can use the following equation:

* d = v₀t (where 'd' is distance, 'v₀' is initial horizontal velocity, and 't' is time)

* Solve for 'v₀':

* v₀ = d / t

* v₀ = 32 m / 9.58 s

* v₀ ≈ 3.34 m/s

Therefore, the initial velocity of the rock was approximately 3.34 m/s.