potential energy at the top = force * distance. Force = mass * acceleration
In this case, acceleration is from gravity, so it is 9.8 m/sec^2
We are given the distance (12m), so:
PE = m * 9.8 * 12
At the bottom, the potential energy has been converted to kinetic (or lost in friction)
KE = 1/2 * m * v^2
We are given v = 14m/sec
KE = 196 * m/2
To find the energy lost, we would subtract the KE at the end from the PE at the start. However, this requires that we know the mass of of the child + sled.
BUT--we are only asked about the percentage loss...
To get this, we can divide KE by PE:
(196 * m/2 ) / (m * 9.8 * 12)
196 / (2*9.8*12) = 0.83333
83% remaining means 17% was lost