Introduction:
When a point charge is released from rest at a distance from an infinite grounded conducting plate, it experiences an electric force due to the charge on the plate. This force causes the charge to accelerate towards the plate. We need to find the time taken by the charge to hit the plate.

Key Concepts:
To solve this problem, we need to consider the following key concepts:
1. Electric force on a point charge: The electric force on a point charge q in an electric field E is given by F = qE.
2. Electric field due to a conducting plate: A grounded conducting plate creates a uniform electric field around it. The electric field lines are perpendicular to the surface of the plate and point towards the plate.
3. Acceleration of a point charge: The acceleration of a point charge q under the influence of an electric force F is given by Newton's second law, F = ma, where m is the mass of the charge.
4. Kinematic equations: We can use the kinematic equations of motion to find the time taken by the charge to hit the plate.

Steps to solve the problem:
1. Determine the electric field due to the grounded conducting plate at the location of the point charge.
2. Calculate the electric force on the point charge using the formula F = qE.
3. Use Newton's second law, F = ma, to find the acceleration of the point charge.
4. Apply the kinematic equation, s = ut + (1/2)at^2, where s is the distance traveled by the charge, u is the initial velocity (which is zero in this case), a is the acceleration, and t is the time taken.
5. Rearrange the equation to solve for t.
6. Substitute the known values into the equation and calculate the time taken.

Conclusion:
By applying the above steps, we can find the time taken by the point charge to hit the grounded conducting plate. The answer will depend on the specific values of the charge, mass, and distance. It is important to note that the result assumes ideal conditions, such as a point charge and an infinite conducting plate.