A projectile leaves the ground at an angle of 60degree to the horizontal.it initial kinetic energy is E. Neglecting air resistance, it kinetic energy at the highest point of the motion is

initial speed = s

initial ke =.5 m s^2 = E

u = s cos 60 forever
at top v=0 so
ke = .5 m u^2 = .5 m s^2 cos^2 60
which is E cos^2 60
= E/4

To determine the kinetic energy at the highest point of the motion, we can make use of the principle of conservation of energy. The initial kinetic energy, E, will be converted into gravitational potential energy at the highest point.

The kinetic energy of the projectile can be calculated using the formula:

K.E. = 1/2 * m * v^2

Where:
K.E. = Kinetic energy
m = Mass of the projectile
v = Velocity of the projectile

Since the problem does not provide information about the mass of the projectile, we can assume it to be m.

At the highest point of the motion, the vertical component of velocity becomes zero, and the kinetic energy is entirely converted into gravitational potential energy. The formula for gravitational potential energy is:

G.P.E. = m * g * h

Where:
G.P.E. = Gravitational potential energy
g = Acceleration due to gravity
h = Height

Since the projectile reaches the same height it was launched at, the gravitational potential energy at the highest point would be equivalent to the initial kinetic energy.

Therefore, the kinetic energy of the projectile at the highest point is E.

To determine the kinetic energy of the projectile at the highest point of its motion, we need to consider the principles of conservation of energy.

At the highest point of its motion, the projectile will have zero vertical velocity. This means that all of its initial kinetic energy will be converted into potential energy.

The initial kinetic energy is given as E. This represents the total mechanical energy (kinetic + potential energy) at the start. Thus, at the highest point, the potential energy will be equal to E.

The formula for potential energy is:

Potential Energy (PE) = mass (m) * gravitational acceleration (g) * height (h)

Since the height at the highest point is the maximum height reached by the projectile, we can calculate it using the knowledge that vertical velocity is zero at this point. The formula for maximum height is:

h = (initial vertical velocity (v₀)²) / (2 * gravitational acceleration (g))

In this case, the initial vertical velocity can be found using trigonometry. The vertical velocity component (v₀y) can be calculated as:

v₀y = initial velocity (v₀) * sin(angle)

Given that the angle is 60 degrees, we can substitute these values into the equation and calculate v₀y.

Finally, we can use the formula for potential energy to find the kinetic energy at the highest point, which is equal to the initial kinetic energy E.