Question

A particle dropped from the top of a tower h high and at the same moment another particle is projected upwards form the bottom. they meet when the upper one has described (1/n) o the distance. show that the velocities when they meet are in the ratio 2:(n-2)band its initial velocity is √((ngh/2).

Answer 1

Upper ball: h/n=(1/2)gt²
or
 t=[(2h)/(ng)]1/2.
And (v1)=gt=[(2gh)/n]1/2.
For the lower ball (h-h/n)=(u2)t +(1/2)gt².
Substitute for t and simplify for (u2). (u2)=[ngh/2]1/2.
By substituting in the (v2)=(u2)+gt
solve for (v2).
Take the ratio (v1) : (v2).