If V₁ is velocity of a body projected from the point A and V₂ is the velocity of a body projected from point B which is vertically below the highest point C. if both the bodies collide, then

Concept Used:

In projectile motion, when two bodies collide, their velocities are related based on their points of projection. The velocity of the body projected from the lower point (B) will be half the velocity of the body projected from the higher point (A).

Calculation:

We need to prove that V₂ = (1/2)V₁.

⇒ According to the problem, the bodies collide at the same height.

⇒ Let the height of point C be H and the height of point B be zero.

⇒ For body projected from point A:

Using the equation of motion:

H = V₁² / (2g)

⇒ For body projected from point B:

Using the equation of motion:

H = V₂² / (2g)

Since both bodies reach the same height H, we can set the equations equal:

V₁² / (2g) = V₂² / (2g)

⇒ V₁² = V₂²

⇒ V₂ = (1/2)V₁

∴ The correct answer is option 2.