Q: A particle is thrown vertically upwards with speed 20 meters per second. Two seconds later, another particle is thrown vertically upwards from exactly the same place. Its initial velocity is also 20 meters per second. How long after the first particle was projected, do the two particles collide? ( Question asked by gloom striken in Yahoo answers).

Ans : Initial velocity of the 1st particle $u_1$=20 m /sec assume acceleration due to gravity g = 10m/$sec^2$.

Maximum height traveled by this particle $H_{max}$= $\frac{u_1^2}{2g}$ = $\frac{20^2}{2\times10}$.

$H_{max}$= $\frac{400}{20}$ ; $H_{max}$= 20m.

Time of ascent $t_a$= u/g =20/10 =2 sec.

i.e when the second object is projected from ground, first object is at maximum height .

When a body is dropped from a  Maximum height or tower of height h and another body is thrown up vertically with a velocity u then they will meet after t=h/u seconds.

t =20/20=1 sec

They will collide after 1sec  after the II particle is projected or 3sec after the I particle is projected.