Answer:
To find the height of the hill, we can use the conservation of energy principle, which states that the initial potential energy of the child and sled at the top of the hill is equal to their final kinetic energy at the bottom of the hill. The potential energy is given by:
PE = mgh
where m is the mass of the child and sled, g is the acceleration due to gravity (9.81 m/s^2), and h is the height of the hill.
The kinetic energy is given by:
KE = (1/2)mv^2
where v is the speed of the child and sled at the bottom of the hill.
Equating the potential and kinetic energies, we have:
mgh = (1/2)mv^2
Canceling the mass, we get:
gh = (1/2)v^2
Solving for h, we have:
h = (1/2) v^2 / g
Substituting the given values, we get:
h = (1/2) (9.94 m/s)^2 / 9.81 m/s^2
h = 5.06 m
Therefore, the height of the hill is 5.06 meters.