Projectile Motion

Projectile motion refers to the motion of an object that is launched into the air and moves under the influence of gravity alone. In this scenario, three particles, A, B, and C, are projected from the top of a tower with the same speed. Particle A is thrown straight upwards, particle B is thrown straight downwards, and particle C is thrown horizontally.

Speed of Particles

The particles A, B, and C hit the ground with speeds va, vb, and vc, respectively. To determine which of the following statements is correct, we need to analyze the motion of each particle separately.

Particle A - Thrown Straight Upwards

When particle A is thrown straight upwards, it experiences a vertical acceleration due to gravity in the opposite direction to its initial velocity. As it reaches the highest point of its trajectory, its velocity becomes zero, and then it starts to fall downwards. The speed with which particle A hits the ground, va, is equal to the speed with which it was initially thrown upwards.

Particle B - Thrown Straight Downwards

When particle B is thrown straight downwards, it experiences a vertical acceleration due to gravity in the same direction as its initial velocity. The acceleration due to gravity increases the speed of particle B as it falls towards the ground. Therefore, the speed with which particle B hits the ground, vb, is greater than the speed with which it was initially thrown downwards.

Particle C - Thrown Horizontally

When particle C is thrown horizontally, it experiences a vertical acceleration due to gravity that does not affect its horizontal motion. The horizontal component of its initial velocity remains constant throughout its motion. As a result, the speed with which particle C hits the ground, vc, is independent of its initial horizontal velocity.

Conclusion

Based on the analysis of the motion of particles A, B, and C, we can conclude the following:

1. The speed with which particle A hits the ground, va, is equal to the speed with which it was initially thrown upwards.
2. The speed with which particle B hits the ground, vb, is greater than the speed with which it was initially thrown downwards.
3. The speed with which particle C hits the ground, vc, is independent of its initial horizontal velocity.

Therefore, the correct statement would depend on the specific options provided, as we need to compare va, vb, and vc.