Final answer:
1. The stone will have a final velocity equal to the square root of twice the acceleration due to gravity multiplied by the height it fell from. 2. The stone will have fallen a distance of (1/2) * g * t^2 after 3 seconds.
Step-by-step explanation:
1. To determine how fast the stone is traveling when it strikes the water, we can use the principle of conservation of energy. Neglecting air resistance, the total energy of the stone remains constant throughout its fall. At the moment it strikes the water, all of its initial potential energy will be converted into kinetic energy. This means that the stone will have a final velocity equal to the square root of twice the acceleration due to gravity multiplied by the height it fell from. The acceleration due to gravity is approximately 9.8 m/s^2.
The formula for the final velocity of the stone is:
v = √(2 * g * h)
Where v is the final velocity, g is the acceleration due to gravity, and h is the height.
2. To find how far the stone will have fallen in 3 seconds, we can use the equations of motion under constant acceleration. Since the stone is dropped, its initial velocity is zero, and its acceleration is the acceleration due to gravity (-9.8 m/s^2). The formula for the distance fallen is:
d = (1/2) * g * t^2
Where d is the distance fallen, g is the acceleration due to gravity, and t is the time.