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Answer :
Final Answer:
The stone's velocity at time t is [tex]\( v = \sqrt{2gh} \)[/tex], and its potential energy is [tex]\( PE = mgh \)[/tex].
Explanation:
When an object is dropped from a height, its velocity at any given time t can be calculated using the kinematic equation [tex]\( v = \sqrt{2gh} \)[/tex], where g is the acceleration due to gravity (approximately 9.8 m/s²) and h is the height. In this scenario, the stone's velocity v at time t is determined by substituting the given values into the equation.
Simultaneously, the potential energy [tex](\( PE \))[/tex] of the stone at any given height is given by[tex]\( PE = mgh \)[/tex], where m is the mass, g is the gravitational acceleration, and h is the height. As the stone is dropped and not thrown, there is no initial velocity, so only gravitational potential energy is considered. The potential energy is directly proportional to both mass and height.
In summary, the stone's velocity depends on the square root of the product of twice the gravitational acceleration and the height. The potential energy, on the other hand, is determined by multiplying the mass, gravitational acceleration, and height. These equations capture the essential physics governing the motion and energy of the stone as it falls into the water.
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