Determine the relation between the kinetic energy of a projectile at maximum height and at initial position for maximum range.

Explanation

Let the mass of the projectile =m and the velocity of projection =v.
Kinetic energy at the time of projection ,`E=1/2mv^2`
For maximum horizontal range, the angle of Projection,
`theta =45^@`
`therefore` At highest point , kinetic energy,
`E.=1/2 m(vcos 45^@)^2 =1/2 mv^2xx1/2 =E/2`