Question

From an inclined plane two particles are projected with same speed at same angle $θ$, one up and other down the plane as shown in figure, which of the following statements is/are correct?

• A. The time of flight of each particle is the same
• B. The particles will collide the plane with same speed
• C. Both the particles strike the plane perpendicularly
• D. The particles will collide in mid air if projected simultaneously and time of flight of each particle is less than the time of collision

Hint:

From an inclined plane two particles are projected with same speed at same angle $θ$, one up and other down the plane as shown in figure, which of the following statements is/are correct? \includegraphics[width=0.5\linewidth]6phy.png \labelfig:placeholder

Answer 1

The Correct Option is A

Let's analyze the motion of the two particles projected from an inclined plane. Both are projected with the same speed and at the same angle θ with respect to the incline, one upwards and the other downwards.

**Key concepts:**

• When a particle is projected from an inclined plane, its motion can be resolved into components parallel and perpendicular to the plane.
• The time of flight for a projectile on an inclined plane depends only on the initial speed, the angle of projection, and the acceleration due to gravity.

**Analysis of Options:**

1. The time of flight of each particle is the same:
   The time of flight for both particles is determined by their components of motion along and perpendicular to the plane. Since both particles are projected with the same speed and angle, the symmetrical nature of the motion ensures the time of flight is indeed the same for both. Hence, this statement is correct.
2. The particles will collide with the plane with the same speed:
   Due to the symmetry and same initial speed, each particle achieves the same speed when it returns to the height of projection upon striking the plane. This option is also correct.
3. Both the particles strike the plane perpendicularly:
   This statement is incorrect because the particles do not have the same angle of impact due to their different directions of initial velocity.
4. The particles will collide in mid-air if projected simultaneously and time of flight of each particle is less than the time of collision:
   This statement is incorrect because when projected at the same time, they will not collide mid-air due to their opposite directions.

**Conclusion:** The correct answer is that the time of flight of each particle is the same.