Point of Projection Acting on the Particle at Maximum Height

At the maximum height of the particle's trajectory, the only force acting on it is the force of gravity. The point of projection, P, does not exert any force on the particle at this point.

Explanation:

When the particle is projected from point P with an initial velocity v0 at an angle θ with the horizontal, it follows a parabolic trajectory. The particle reaches its maximum height when its vertical velocity component becomes zero. At this point, the particle momentarily stops moving vertically and starts descending.

The forces acting on the particle at this point are the gravitational force (mg) and the normal force (N) exerted by the ground. The normal force acts perpendicular to the surface of the ground and prevents the particle from sinking into the ground.

However, the point of projection, P, does not exert any force on the particle at its maximum height. The force of projection is applied at the moment of projection, giving the particle its initial velocity v0. Once the particle is in motion, it follows a projectile motion under the influence of gravity.

During its ascent, the gravitational force acts in the downward direction, opposing the particle's upward motion. At the maximum height, the vertical velocity component becomes zero, and the gravitational force pulls the particle downward, causing it to descend.

The point of projection, P, is stationary and does not exert any additional force on the particle. It is merely the starting point from where the particle is projected with an initial velocity. The motion of the particle is determined solely by the forces acting on it, primarily the force of gravity.

In conclusion, at the maximum height of the particle's trajectory, the point of projection, P, does not exert any force on the particle. The only force acting on the particle at this point is the force of gravity, which causes it to descend back to the ground.