Final answer:
To find the distance below the bridge that the water is, we can use the equations for gravitational potential energy and kinematic motion. The stone is dropped from rest, so its initial velocity is 0. By applying the principle of conservation of energy, we can determine the speed of the stone just before it hits the water. Using the equation for distance fallen in free fall, we can find the height of the bridge above the water.
Step-by-step explanation:
To solve the problem, we can use the principle of conservation of energy. When the stone is dropped, it only has potential energy due to its height above the water. As it falls, this potential energy is converted into kinetic energy, causing the stone to accelerate. When the stone hits the water, all of its potential energy has been converted into kinetic energy.
We can use the equation for gravitational potential energy, PE = mgh, where m is the mass of the stone, g is the acceleration due to gravity, and h is the height of the bridge above the water. We can then equate this potential energy to the kinetic energy of the stone just before it hits the water, which is given by KE = 0.5mv^2, where v is the velocity of the stone.
Using these equations and solving for v, we can find the speed of the stone just before it hits the water. In this case, the stone is dropped from rest, so its initial velocity is 0. We can plug in the given values, such as the time of 4.0 seconds, into the equations to find the answer.
By using the equation h = 0.5gt^2, which represents the distance fallen by an object in free fall, we can find the height of the bridge above the water.