Two objects are thrown vertically upwards with the same velocity v from the same point. If the second object is thrown a time T later than the first object, when will the two objects collide with each other?

Explanation

Let us assume that at a time t after throwing the first object the two will collide with each other at a height h above the initial point. So, for the first and the second objects,
`h = vt - (1)/(2)"gt"^(2)" ""and"" "h = v (t-T) - (1)/(2)g (t-T)^(2)`
`:." " vt - (1)/(2)"gt"^(2) = v(t-T) - (1)/(2)g(t-T)^(2)`
=` vt -vT- (1)/(2)"gt"^(2)- (1)/(2)gT^(2)+"gtT"`
or`" "vT +(1)/(2)gT^(2) = "gtT" " ""or",t = (v)/(g)+(T)/(2).`