When a projectile is launched at an angle to the horizontal without air resistance, its kinetic energy changes throughout its motion. At the highest point of its trajectory, the projectile's kinetic energy will be a fraction of its initial kinetic energy, E.
At the highest point of motion, the projectile reaches its maximum height and momentarily comes to a stop before changing direction and falling back down. At this point, all of its initial kinetic energy has been converted to gravitational potential energy, neglecting air resistance.
The equation for gravitational potential energy is given by:
Potential Energy = m * g * h
Where: m is the mass of the projectile, g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth), and h is the height reached by the projectile.
At the highest point, the height h is the maximum height attained by the projectile. The potential energy at this point is equal to the initial kinetic energy E, since they have been converted from one form to another. Therefore:
E = m * g * h
Solving for h:
h = E / (m * g)
So, at the highest point of the motion, the kinetic energy of the projectile in terms of E is 0, as all the initial kinetic energy has been converted to potential energy.