A particle is dropped from the top a tower h metre high and at the same moment another particle is projected upward from the bottom. They meet the upper one has descended a distance h//n . Show that thevelocities of the two when they meet are in the ratio 2: (n-2) and that the initial velocity of the particle projected upis sqrt((1//2))n gh.

A particle is dropped from the top a tower h metre high and at the sam

1.	A particle is dropped from the top a tower h metre high and at the same moment another particle is projected upward from the bottom. They meet the upper one has descended a distance h//n . Show that thevelocities of the two when they meet are in the ratio 2: (n-2) and that the initial velocity of the particle projected upis sqrt((1//2))n gh.
Answer» Solution :`t =sqrt((2h)/(NG)), H-(h)/(n)=ut-(1)/(2) G t^(2)` `rArr u=(h)/(t) =sqrt((nhg)/(2))` `v_(1)=g t, v_(2)=u-g t, (v_(2))/(v_(1)) =(u-g t)/(g t) =(u)/(g t)-1` `rArr (v_(2))/(v_(1)) =(h)/(g t^(2) )-1 =(hng)/(g2h)-1 rArr (v_(1))/(v_(2))=(2)/(n-2). ` .