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**divine_mail** A particle of mass *m *is projected vertically upwards with speed *u* and when it reaches its greatest height a second particle of mass 2*m* is projected vertically upward with speed 2*u* from the same point as the first.

prove that the time elapses between the projection of the second particle and its collision with the first is *u/4g*

find the height above the ground at which this occurs

if on collision thwe particles coalesce, prove that the combined particle will reach a greates height of *19u^2/18g*

*many thanks*