A child and a sled with a combined mass of 50.0 kg slide...

A child and a sled with a combined mass of 50.0 kg slide down a frictionless slope. If the sled starts from rest and has a speed of 3.00 $\mathrm{m} / \mathrm{s}$ at the bottom, what is the height of the hill?

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Key Concepts

Conservation of Mechanical Energy

This principle states that in the absence of non-conservative forces (such as friction), the total mechanical energy of a system remains constant. That means the sum of kinetic energy and gravitational potential energy at one point is equal to the sum at any other point in the system.

Gravitational Potential Energy

This is the energy stored in an object due to its position in a gravitational field, usually quantified by the product of the object's mass, gravitational acceleration, and height (mgh). It represents the work done against gravity to elevate the object.

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion, calculated by the formula 1/2 mv². It expresses the energy resulting from the movement of the mass.

Energy Conversion on a Frictionless Slope

In scenarios like a frictionless slope, gravitational potential energy is converted entirely into kinetic energy as the object descends. This conversion allows one to relate the height of the hill to the final speed of the object using energy conservation principles.

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