A particle is dropped from a height and another particle is thrown in ...
For both cases,

Because vertical downward component of velocity will be zero for both the particles.
A particle is dropped from a height and another particle is thrown in ...
Explanation:
When a particle is dropped from a height, it falls freely under the influence of gravity. The only force acting on it is the force of gravity, which causes it to accelerate downwards.
When a particle is thrown horizontally with a certain speed, it also experiences the force of gravity but it also has an initial horizontal velocity. The horizontal velocity remains constant throughout its motion.
Time of Flight:
Since both particles are starting from the same height, they will take the same amount of time to reach the ground. This is because the force of gravity acts vertically downwards and does not affect the horizontal motion.
Horizontal Distance:
The particle thrown horizontally will cover some horizontal distance while falling vertically. This horizontal distance is determined by the horizontal velocity and the time of flight. Since the horizontal velocity is constant, the distance covered will be the same for both particles.
Conclusion:
Based on the above observations, we can conclude that both particles will reach the ground simultaneously. The particle dropped vertically will fall straight down, while the particle thrown horizontally will cover some horizontal distance before reaching the ground, but they will both reach the ground at the same time.
Therefore, the correct statement is option 'A': Both particles will reach the ground simultaneously.