A particle of mass is projected with a speed from the ground at angle is w.r.t. horizontal . When it has reached its maximum height, it collides completely in elastically with another particle of the same mass and velocity . The horizontal distance covered by the combined mass before reaching the ground is:
Step 1: Given data and assumptions.
Mass of the particle
Projectile angle,
Initial velocity
Step 2: Finding the horizontal velocity of the combined mass.
We know that,
According to the law of conservation of momentum,
Where, is initial momentum, and is final momentum.
[As it collides elastically, a mass will stick to the other mass]
Where, is the mass of the particle, is the initial velocity of the particle, and is the final velocity.
….
Step 3: Find the time required to reach the maximum height
Since,
Vertical maximum range,
Where, is time to reach the maximum height and is the acceleration due to gravity.
……
Step 4: Finding the horizontal distance traveled by the combined mass
Since the horizontal range after collision
[ From]
Hence, option A is Correct.