Answer:
Top: PE = max, KE = 0
Middle: PE = half, KE = half
Bottom: PE = 0, KE = max
Explanation:
The potential energy of an object is the energy possessed by the object due to its location; it is given by
where
m is the mass of the object
g is the acceleration due to gravity
h is the height of the object from the ground
The kinetic energy of an object is the energy possessed by the object due to its motion; it is given by
where
v is the speed of the object
Now we analyze the three situations for the boy on the bycicle:
Top of the hill: here h (the height) is maximum, so the potential energy is maximum, while the speed is zero, therefore the kinetic energy is zero.
Middle of the hill: here h (the height) is half of the initial value, therefore the potential energy is also half of the initial potential energy. According to the law of conservation of energy, the total mechanical energy (potential+kinetic) is constant: this means that also the kinetic energy is half of the initial potential energy.
Bottom of the hill: here h is zero, therefore the potential energy is now zero. As a result, all the mechanical energy has been converted into kinetic energy, therefore the kinetic energy is maximum and it is equal to the potential energy of the boy when he was at the top.