Introduction:

When a particle is projected at an angle to the horizontal, its kinetic energy (K.E) changes as it moves through different points in its trajectory. In this case, the particle is projected at an angle of 60 degrees to the horizontal, and we are interested in understanding the kinetic energy at the highest point.

Explanation:

1. Initial Kinetic Energy:
- When the particle is initially projected, it possesses kinetic energy due to its motion.
- The initial kinetic energy, denoted as K, is given by the formula K = 0.5 * m * v^2, where m is the mass of the particle and v is its initial velocity.
- The initial velocity can be broken down into horizontal and vertical components using trigonometry.
- The horizontal component of velocity remains constant throughout the motion, while the vertical component changes due to the effect of gravity.

2. Highest Point:
- As the particle moves along its trajectory, it reaches a point where its vertical velocity becomes zero.
- At this highest point, the particle momentarily stops moving upwards before it starts descending.
- At the highest point, the particle's total mechanical energy is solely in the form of potential energy, as its kinetic energy becomes zero.

3. Kinetic Energy at the Highest Point:
- Since the particle has come to a temporary stop at the highest point, its kinetic energy is zero.
- At this point, all the initial kinetic energy of the particle has been converted into potential energy.
- The potential energy can be calculated using the formula PE = m * g * h, where m is the mass of the particle, g is the acceleration due to gravity, and h is the height of the particle at the highest point.
- The potential energy at the highest point is equivalent to the initial kinetic energy K.

Conclusion:

In summary, when a particle is projected at an angle to the horizontal, its kinetic energy changes throughout its trajectory. At the highest point, the particle's kinetic energy becomes zero, and all the initial kinetic energy is converted into potential energy.