An object has kinetic energy E when it is projected at an angle of maximum range then at the highest point of its path the kinetic energy E of the object will be
Kinetic Energy, E = ½mv2
At the highest point, vertical component of velocity becomes zero and only the horizontal component is left that is given by
ux = u cosθ
θ = 45° (Since at maximum range angle will be 45)
, so cosθ = 1/√2
ux = u/√2
Kinetic energy E at the highest point = ½m(u/√2)2 = E/2