Standing on the side of a bridge, a person uses a sling shot pulled back 20 centimeters to shoot a rock with a mass of 250 grams almost straight up into the air which then falls into the water below. The pebble traveled a maximum height of 4.0 meters above the level of the person's hand, which is 8.5 meters above the water. Find the spring constant of the elastic band of the sling shot and the speed at which the pebble hits the water. Ignore air resistance. Solve using conservation of energy principles and the various forms of kinetic and potential energies.

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Spring Potential Energy

The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The potential energy is the measure of the net work done by or on the body. The spring potential energy is the potential energy stored due to the deformation of an elastic spring and this elasticity is due to the stretched spring. The elasticity is the ability of a solid-state matter to come back to its equilibrium position or original position after any kind of external force is acted on it. It is also known as Elastic potential energy. The potential energy here is caused due to the displacement of the spring from its equilibrium position to another position and this potential energy is equal to the net work done due to the stretching of the spring. It also resembles the same mechanics of the oscillation of a simple pendulum, where due to the external force, the object moves from its equilibrium position to its maximum ends and the periodic motion continues till it comes back to the equilibrium position to rest.