To determine the velocity halfway through the fall of a stone, we can use the equations of motion under constant acceleration. In this case, the stone is falling freely under the influence of gravity, which produces a constant acceleration equal to the acceleration due to gravity, denoted as 'g' and approximately equal to 9.8 m/s².
We'll assume the positive direction is downward, and we'll measure distances and velocities relative to this direction.
Given: Initial height (h₁) = 250.0 m (above the ground) Acceleration due to gravity (g) = 9.8 m/s²
To find the velocity halfway through the fall, we can use the following equation:
v² = u² + 2as
where: v = final velocity u = initial velocity (which is 0 since the stone is initially at rest) a = acceleration due to gravity (g) s = displacement (half the total distance)
First, let's calculate the displacement (s) halfway through the fall: s = h₁ / 2 s = 250.0 m / 2 s = 125.0 m
Now, we can calculate the velocity (v) halfway through the fall using the equation:
v² = u² + 2as
Since the stone starts from rest (u = 0), the equation simplifies to:
v² = 2as
Plugging in the values:
v² = 2 × 9.8 m/s² × 125.0 m v² = 2450 m²/s²
Taking the square root of both sides:
v = √2450 m/s v ≈ 49.5 m/s
Therefore, the velocity halfway through the fall is approximately 49.5 m/s (downward).