Q. A particle of mass m is dropped from a height h above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of $\sqrt{2gh}$. If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of $\sqrt{\frac{h}{g}}$ is :
Solution:
Particles will collide after time $t_{0}=\frac{h}{\sqrt{2\,gh}}$
at collision, $v_{A}=gt_{0}\,v_{B}=u_{B}-gt_{0}$
$\Rightarrow v_{A}=-v_{B}$
Time taken by combined mass to reach theground
time $=\sqrt{\frac{2\times3h / 4}{g}}=\sqrt{\frac{3h}{2g}}$
