A particle is dropped from the top of a tower h meter high and simultaneously a particle is projected upwards from bottom. They meet when the upper one has descended 1/n of the distance. find the initial velocity of the lower particle?
The initial velocity of the lower particle was
So, you know that you're dealing with two particles, one at the top of a tower that's h meters high, and the other one on the bottom.
Moreover, you know that if you drop the top particle with no initial velocity and launch the bottom particle with an initial velocity equalto
For the upper particle, the distance it travelled can be written as
The bottom particle will travel a distance of
For the bottom particle you can write
Since the two particles meet up at this point, the time of flight for both particles must be equal.
Plug this into equation
Rearrange to isolate
This is equivalent to