Final answer:
To find the height of the hill, we would use energy conservation, where the gravitational potential energy at the top is equal to the kinetic energy at the bottom. Without the velocity given, we cannot solve for the specific height, but with it, we would use the formula h = (v^2) / (2g) to calculate the height.
Step-by-step explanation:
To answer this student's question, we must apply the principles of energy conservation. The child and sled system's gravitational potential energy (PE) at the top of the hill will be entirely converted into kinetic energy (KE) at the bottom, assuming a frictionless slope.
Since the sled starts from rest, its initial KE is zero, and its initial PE can be expressed as PE = mgh, where m is the mass, g is the acceleration due to gravity (9.81 m/s2), and h is the height of the hill.
At the bottom, all of the PE has been converted into KE, which is given by KE = (1/2)mv2, where v is the velocity at the bottom of the hill. Now, we can set the initial PE equal to the final KE to solve for h.
Thus, the formula becomes mgh = (1/2)mv2. The mass m cancels out, which simplifies the equation to gh = (1/2)v2. Solving for h gives h = (v2)/(2g).
To find the specific height h, we would need the velocity v of the sled at the bottom (which is missing in the question). Once we have the velocity, we would plug it into the formula to get the height.