Answer to Question #190575 in Classical Mechanics for Mmwicks

Question

An object is vertically projected at u velocity ..After t time another one is projected at the same velocity. Show the meeting time is (t/2 + u/g) after the first object projected .

Answer 1

$t_{up}=\frac ug,~s_{up}=\frac{u^2}{2g},$

$s=s_{up}-s'=\frac{u^2}{2g}-u(\frac ug-t)+\frac{gt^2}{2}=ut-\frac{u^2}{2g}+\frac{gt^2}{2},$

$v'=u-g(\frac ug-t)=gt,$

$gtt'-\frac{gt'^2}{2}=s-\frac{gt'^2}{2},$

$t'=\frac{s}{gt}=\frac ug-\frac t2,$

$T=t+t'=\frac t2+\frac ug.$