c) How does the mechanical energy Eat of the child-sled-Earth system change while traveling down the hill? Explain why

## Step 1<br />The problem involves the principle of conservation of mechanical energy. Mechanical energy is the sum of kinetic energy and potential energy. <br /><br />## Step 2<br />When the child-sled-Earth system is at the top of the hill, it has maximum potential energy and minimum kinetic energy. This is because it is at the highest point and has not started moving, so its speed is zero.<br /><br />## Step 3<br />As the system starts moving down the hill, the potential energy decreases because the height decreases. However, the kinetic energy increases because the speed increases.<br /><br />## Step 4<br />The total mechanical energy of the system remains constant if we ignore air resistance and friction. This is because the decrease in potential energy is exactly balanced by the increase in kinetic energy.