A particle of mass is dropped from a height above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of . If they collide head on completely in elastically, the time taken for the combined mass to reach the ground, in units of is:
Step1: Given data and assumptions.
Mass of particle ,
Mass of particle ,
Height from the ground of particle
Speed of the particle
Time taken by combined mass to reach the ground
Step2: Height from ground at time of collision.
We know that,
Time for collision
Now,
After time , velocity of particle .
Where is the final velocity, is the initial velocity, is the acceleration due to gravity
And velocity of particle
Again,
According to the law of conservation of linear momentum.
And
height from ground at time of collision,
Step3: Finding the value of time
Now the time taken for the combined mass to reach the ground
Hence, option A is correct. The time taken for the combined mass to reach the ground, in units of is